---
title: "Temporal network tools in statnet: networkDynamic, ndtv and tsna"
author: "Skye Bender-deMoll"
date: "04/05/2016"
output:
  html_document:
    fig_width: 8
    highlight: kate
    theme: cosmo
    toc: yes
    css: custom.css
  pdf_document:
    toc: yes
---
```{r setup, include=FALSE,cache=FALSE}
library(knitr)
knitr::opts_chunk$set(comment='') #,cache=TRUE)
library(animation)
#library(printr)
```

![](http://skyeome.net/wordpress/wp-content/uploads/2015/05/proxTimeineWithInf.png)

# Introduction to this workshop

This workshop will explore the key features of the open-source R packages that `statnet` suite provides for working with dynamic (longitudinal) network data:

 * `networkDynamic`  (Butts, et al) extends the `network` package to provide data structures for edge, vertex, and attribute dynamics
 * `ndtv` (Network Dynamic Temporal Visualization) provides tools for visualizing and animating changing network structure
 * `tsna` provides basic temporal social network analysis statistics, in part by leveraging algorithms provided by the `ergm`, `relevent` and `sna` packages.
 * `networkDynamicData` includes several dynamic network data sets shared by multiple authors. 
 
 There is much more material in the workshop than we will be able to cover in three hours, so this document is also intended to serve as a reference as well. 
 
 This work was supported by grant R01HD68395 from the National Institute of Health.


## Workshop prerequisites

  * Familiarity with the R statistical software.  This tutorial does not cover basics of how to use and install R.
  * Functioning R installation and basic statnet packages already installed. (Instructions on installing R and statnet are located here https://statnet.org/trac/wiki/Installation.)  RStudio recommended. 
  * Familiarity with general network and SNA concepts
  * Experience with statnet packages and `network` data structures preferred but not necessary. (A tutorial providing "An Introduction to Network Analysis with R and statnet"" is located here: https://statnet.org/trac/wiki/Resources)
  * A working internet connection (we will install some libraries and download data sets)

# A Quick Demo

Lets get started with a realistic example. We can render a simple network animation in the R plot window (no need to follow along in this part) 

First we load the package and its dependencies.
```{r,message=FALSE,cache=FALSE}
library(ndtv)
```
Now we need some dynamic network data to explore. The package includes an example network data set named `short.stergm.sim` which is the output of a toy STERGM model based on Padgett's Florentine Family Business Ties dataset simulated using the `tergm` package. (Using the tergm package to simulate the model is illustrated in a later example.)  

```{r}
data(short.stergm.sim)
```

## Render a network animation in a plot window
If we want to get a quick visual summary of how the structure changes over time, we could render the network as an animation.

```{r,fig.keep='none',message=FALSE,results='hide',cache=TRUE}
render.animation(short.stergm.sim)
```

And then play it back in the R plot window as many times as we want
```{r,fig.show='hide',cache=TRUE}
ani.replay()
```


## Render a network animation as an interactive web page
We can also present a similar animation as an interactive HTML5 animation in a web browser. 
```{r,message=FALSE,results='hide',cache=FALSE}
render.d3movie(short.stergm.sim)
```

This should bring up a browser window displaying the animation.  In addition to playing and pausing the movie, it is possible to click on vertices and edges to show their ids, double-click to highlight neighbors, and zoom into the network at any point in time. 

## Render a network in markdown document or RStudio
By changing the output slightly, we can embed directly in an Rmarkdown document or RStudio plot window
```{r,message=FALSE,cache=FALSE}
render.d3movie(short.stergm.sim,output.mode = 'htmlWidget')
```


## Plot a static "filmstrip" sequence

An animation is not the only way to display a sequence of views of the network.  We could also use the `filmstrip()` function that will create a "small multiple" plot using frames of the animation to construct a static visual summary of the network changes.

```{r,cache=TRUE}
filmstrip(short.stergm.sim,displaylabels=FALSE)
```

## Plot a "timePrism" projection
If were to select some of the 'small multiple' frames from the movie and stack them up in layers of time, we will have an illustrative 'timePrism' projection of the network. This view introduces some clutter and distortion, but includes both some time and some relational information
```{r,message=FALSE}
compute.animation(short.stergm.sim)
timePrism(short.stergm.sim,at=c(1,10,20),
          displaylabels=TRUE,planes = TRUE,
          label.cex=0.5)
```


## Plot a timeline
If we want to focus solely on the relative durations of events, we can view the dynamics as a `timeline` by plotting the active spells of edges and vertices.
```{r}
timeline(short.stergm.sim)
```

In this view, only the activity state of the network elements are shown--the structure and network connectivity is not visible. The vertices in this network are always active so they trace out unbroken horizontal lines in the upper portion of the plot, while the edge toggles are drawn in the lower portion.  

## Plot a proximity timeline
We are experimenting with a form of timeline or "phase plot". In this view vertices are positioned vertically by their geodesic distance proximity.  This means that changes in network structure deflect the vertices' lines into new positions, attempting to keep closely-tied vertices as neighbors. The edges are not shown at all in this view. 

```{r,message=FALSE,cache=TRUE}
proximity.timeline(short.stergm.sim,default.dist=6,
          mode='sammon',labels.at=17,vertex.cex=4)
```

Notice how the bundles of vertex lines diverge after time 20, reflecting the split of the large component into two smaller components. 

## Print tabular data

Of course we can always display the edge (or vertex) spells directly in a tabular form using the various utilities in the `networkDynamic` package. 

```{r}
head( as.data.frame(short.stergm.sim) )
```

*****
**Question:** What are some strengths and weakness of the various views?

*****

*****
**Exercise:** Load the saved version of `short.stergm.sim`. Are there any edges that are present for the entire time period from 0 until 25?


```{r}
data(short.stergm.sim)
spls<-as.data.frame(short.stergm.sim)
spls[spls$duration==25,]
```

*****

## Compute some basic temporal stats

Load up the `tsna` (Temporal Social Network Analysis) library
```{r,message=FALSE}
library(tsna)
```

How many edges form at each time step for the `short.stergm.sim`?  Conveniently, the values are returned as a time series, `plot` already knows how to handle them.
```{r}
tEdgeFormation(short.stergm.sim)

plot( tEdgeFormation(short.stergm.sim) )
```


## Compute static graph-level sna measure as a time series

The `tsna` package provides wrapper functions that make it easy to compute a time series using statistics from the `sna` package or `ergm` terms.  For example, we can use the `gtrans` function to compute transitivity in the network. 

```{r}
plot( tSnaStats(short.stergm.sim,'gtrans') )
```


## Find temporally reachable paths

We can quickly compute the earliest times a journey from vertex 13 can reach the rest of the network traveling forward along time-respecting paths in the network.  And then plot this path as an overlay on the aggregate network.

```{r}
path<-tPath(short.stergm.sim,v = 13,
            graph.step.time=1)

plotPaths(short.stergm.sim,
          path,
          label.cex=0.5)
```


# The Basics

Now that we've had a quick tour of some of what we will cover in the tutorial, lets get things set up and explain what is going on. 

## Installing the packages 

The `ndtv` (Bender-deMoll 2013) package relies on many other packages to do much of the heavy lifting, especially `animation` (Xie Y 2012) and `networkDynamic` (Butts et. al. 2012) which provides its input objects. Web animations can be created and viewed on computers with modern web browsers without additional components using the built-in `ndtv-d3` l.  However, `ndtv` does require some non-R external dependencies (`FFmpeg` or `avconv`) to save movies as video files, and Java to be able to use some of the better quality layout algorithms. These are discussed in a later section.

The core use-case for development is examining the output of statistical network models (such as those produced by the tergm (Krivitsky and Handcock 2015) package in statnet (Handcock et. al. 2003b) and simulations of disease spread across networks. The design philosophy is that it should be easy to do basic things, but lots of ability to customize.

R can automatically install the packages `ndtv` depends on when `ndtv` is installed. So open up your R console, and run the following command:
```{r,message=FALSE,results='hide'}
install.packages('ndtv',repos='http://cran.us.r-project.org', 
                 dependencies=TRUE)
library(ndtv) # also loads animation and networkDynamic
```

We will also use the `tsna` package for temporal SNA, so let's install and load that now as well.  It will bring along the `sna` and `ergm` packages

```{r,message=FALSE,results='hide'}
install.packages('tsna',repos='http://cran.us.r-project.org', 
                 dependencies=TRUE)
library(tsna)
```


## Understanding how networkDynamic works

Lets take quick tour of a `networkDynamic` object and work through some example in more detail to explain what is going on. Please follow along by running these commands in your R terminal. 


We are going to build a simple `networkDynamic` object "by hand" and then peek at its internal structure and visualize its dynamics. Note that the `networkDynamic()` command provides utilities for constructing dynamic networks from real data in various data formats, see some the later examples. 

### Activating a static network

First, we will create a static network with 10 vertices
```{r}
wheel <- network.initialize(10)
class(wheel)
```

Next we add some edges with activity spells.  The edges' connections are determined by the vector of `tail` and `head` vertex ids, and the start and ending time for each edge is specified by the `onset` and `terminus` vectors.
```{r}
add.edges.active(wheel,tail=1:9,head=c(2:9,1),onset=1:9, terminus=11)
add.edges.active(wheel,tail=10,head=c(1:9),onset=10, terminus=12)
```

Adding active edges to a network has the side effect of converting it to a `networkDynamic`. Lets verify it.

```{r}
class(wheel)
print(wheel)
```

Notice that the object now has a class of both `networkDynamic` and `network`.  All `networkDynamic` objects are still `network` objects, they just include additional special attributes to store time information.  The print command for `networkDynamic` objects includes some additional info about the time range of the network and then the normal output from `print.network`.


Once again, we can peek at the edge dynamics by transforming a view of the network into a `data.frame`.
```{r}
as.data.frame(wheel)
```

When we look at the output `data.frame`, we can see that it did what we asked. For example, edge id 1 connects the "tail" vertex id 1 to "head" vertex id 2  and has a duration of 10, extending from the "onset" of time 1 until the "terminus" of time 11. 

It is important to remember that `dynamicNetwork` objects are also static `network` objects.  So all of the `network` functions will still work, they will just ignore the time dimension attached to edges and vertices. For example, if we just `plot` the network, we see all the edges that ever exist (and realize why the network is named "wheel"). 
```{r}
plot(wheel)
```

### Extracting from a dynamic network

If we want to just see the edges active at a specific time point, we could first extract a snapshot view of the network at a single point in time and then plot it. 
```{r}
plot(network.extract(wheel,at=1))
```

But we can also extract a view of the network covering an interval of time.
```{r}
plot(network.extract(wheel,onset=1,terminus=5))
```


The `network.extract` function is one of the many tools provided by the `networkDynamic` package for storing and manipulating the time information attached to networks without having to work directly with the low-level data structures. The command `help(package='networkDynamic')` will give a listing of the help pages for all of the functions.   

*****
**Exercise:** Use the help function to determine the difference between the `network.extract()` and `network.collapse()` functions

*****

### Under the hood: spells and the 'activity' attribute

A potentially confusing point about the language we use when expanding from the static `network` object to a dynamic `networkDynamic` context is that "edge" now means something like "a container for all of the realizations of a tie between (usually a pair of) vertices". An "edge-spell" refers to a specific period of time over which the edge is known to be active. 

The edge-spells for each edge are stored in an attribute named `activity` as a two-column matrix of starting and ending times (which we refer to as "onset" and "terminus").  For many tasks, we would use higher-level methods like `get.edgeIDs.active()` but, we can access timing information directly using `get.edge.activity`.

Print the edge activity of edge ids 1 and 2
```{r}
get.edge.activity(wheel)[1:2]
```

So the `networkDynamic` object is not a big list of matrices for each discrete time point, and it is not even a list of networks. It can comfortably capture networks as multiple waves, but it can also store continuous time networks where each tie has its own timestamp.  The help page `?activity.attribute` is a good place to learn more detail about how the `networkDynamic` package represents dynamics.


Since the static plot, doesn't show us which edges are active when, lets annotate it by labeling edges with their onset and termination times so we can check that it constructed the network we told it to.

Make a list of labels for each edge, pasting the onset and terminus time together.
```{r}
elabels<-lapply(get.edge.activity(wheel),
                function(spl){
                  paste("(",spl[,1],"-",spl[,2],")",sep='')
                })
```

Plot the network, labeling each edge using the list of times.
```{r}
plot(wheel,displaylabels=TRUE,edge.label=elabels,
     edge.label.col='blue') 
```

*****
**Question:** Why is this edge labeling function not general enough for some networks? (Hint: do edges always have a single onset and terminus time?)

*****


Now lets render the network dynamics as a movie and play it back so that we can visually understand the sequence of edge changes. 
```{r,message=FALSE,fig.keep='none'}
render.animation(wheel) # compute and render
ani.replay()
```

Hopefully, when you play the movie you see a bunch of labeled nodes moving smoothly around in the R plot window, with edges slowly appearing to link them into a circle. Then a set of "spoke" edges appear to draw a vertex into the center, and finally the rest of the wheel disappears. An example of the animation rendered as a movie is located at http://statnet.org/movies/ndtv_vignette/wheel.mp4.

### Transforming between representations

Later sections of this tutorial give more complete examples of importing real network data from various formats.  For the moment, we can quickly through translating from one type of representation to another. 

******
**Excercise:**  If the three adjacency matrices below represent three time points of a network, what would the corresponding timed-edgelist representation be?
```
t0:       t1:       t2:
0 1 0     0 1 0     0 0 0
0 0 0     0 1 0     0 1 0
1 0 0     0 0 0     0 1 0
````

```{r}
# create a network object from each matrix
t0<-as.network(matrix(c(0,1,0,
                        0,0,0,
                        1,0,0),ncol=3,byrow=TRUE))

t1<-as.network(matrix(c(0,1,0,
                        0,1,0,
                        0,0,0),ncol=3,byrow=TRUE))

t2<-as.network(matrix(c(0,0,0,
                        0,1,0,
                        0,1,0),ncol=3,byrow=TRUE))
# convert a list of networks into networkDynamic object
tnet<-networkDynamic(network.list=list(t0,t1,t2))
# print the networkDynamic object as a timed edgelist
as.data.frame(tnet)[,1:4]

```

******

******
**Excercise:**  Create a `networkDynamic` object from the timed edgelist below. Assume columns are onset, terminus, tail, head.

```
0	1	3	1
0	2	1	2
2	3	3	2
```
```{r}
tel<-matrix(c(0,1,3,1,
              0,2,1,2,
              2,3,3,2),ncol=4,byrow=TRUE)
tnet<-networkDynamic(edge.spells=tel)
```

******

### Data utilities 

The `networkDynamic` package provides many utilities for querying, constructing, and manipulating dynamic network data. Since we won't have time to delve into them all here, I'll just point out some of the help topics for features that may be easy to overlook, and suggest referring to the help index and `browseVignette(package='networkDynamic')`.

* `?networkDynamic` Convert various forms of network timing information (including toggles and matrices) into networkDynamic objects
* `?adjust.activity` Adjust and transform the activity ranges in all of the spells of a networkDynamic object.
* `?persistent.ids` Create and query 'persistent ids' of networks that will remain constant as network size changes due to extraction.
* `?reconcile.activity`  Clean up messy input data by modifying the activity spells of vertices to match incident edges or the other way around.
* `?timeProjectedNetwork`  Construct a time-projected ("multi-slice") network representation by binning a longitudinal network and linking time points with "identity arcs".
  
## Understanding how ndtv works

As we saw in the wheel example, creating the animations is simple right? Hopefully most of the complexity was hidden under the hood, but it is still useful to understand what is going on. At its most basic, rendering a movie consists of four key steps:

1. Determining appropriate parameters (time range, aggregation rule, etc)
2. Computing layout coordinates for each time slice
3. Rendering a series of plots for each time slice
4. Replaying the cached sequence of plots (or writing to a file on disk)

When we called `render.animation()` we asked the package to create an animation for `wheel` but we didn't include any arguments indicating what should be rendered or how, so it had to make some educated guesses or use default values. For example, it assumed that the entire time range of the network should be rendered and that we should use the Kamada-Kawai layout to position the vertices.
    
The process of positioning the vertices was managed by the `compute.animation()` function which stepped through the `wheel` network and called a layout function to compute vertex coordinates for each time step. 

Next, `render.animation()` looped through the network and used `plot.network()` to render appropriate slice network for each time step.  It calls the `animation` package function `ani.record()` to cache the frames of the animation. Finally, `ani.replay()` quickly redrew the sequence of cached images in the plot window as an animation.

The `render.d3movie()` works along the same lines, but in step three the 'render' it stores at each step is a description of the time slice in a web data language (JSON), and in step four it feeds the data into an web app (the ndtv-d3 player) which it then displays. 

### Controlling the animation processing steps

For more precise control of the processes, we can call each of the steps in sequence and explicitly set the parameters we want for the rendering and layout algorithms. First we will define a `slice.par`, which is a list of named parameters to specify the time range that we want to compute and render.

```{r}
slice.par=list(start=1, end=12, interval=1, aggregate.dur=1,
              rule='latest')
```

Then we ask it to compute the coordinates for the animation, passing in the `slice.par` list. The `animation.mode` argument specifies which algorithm to use.
```{r}
compute.animation(wheel,animation.mode='kamadakawai',slice.par=slice.par)
```

The x and y coordinates for plotting each time point are now stored in the network. 
```{r}
list.vertex.attributes(wheel)
# peek at x coords at time 4
get.vertex.attribute.active(wheel,'animation.x',at=4)
```

We can see that in addition to the standard vertex attributes of `na` and `vertex.names`, the network now has two dynamic "TEA" attributes for each vertex to describe its position over time. The `slice.par` argument is also cached as a network attribute so that later on `render.animation()` will know what range to render.

Since the coordinates are stored in the network, we can collapse the dynamics at any time point, extract the coordinates, and plot it:
```{r}
wheelAt8<-network.collapse(wheel,at=8)
coordsAt8<-cbind(wheelAt8%v%'animation.x',wheelAt8%v%'animation.y')
plot(wheelAt8,coord=coordsAt8)
```

This is essentially what `render.animation()` does internally.  The standard network plotting arguments are accepted by `render.animation` (via `...`) and will be passed to `plot.network()`:

```{r,fig.keep='none',message=FALSE}
render.animation(wheel,vertex.col='blue',edge.col='gray',
                 main='A network animation')
```

`render.animation()` also plots a number of in-between frames for each slice to smoothly transition the vertex positions between successive  points. We can adjust how many "tweening" interpolation frames will be rendered which indirectly impacts the perceived speed of the movie (more tweening means a slower and smoother movie). For no animation smoothing at all, set `tween.frames=1`.

```{r,fig.keep='none',message=FALSE}
render.animation(wheel,render.par=list(tween.frames=1),
                 vertex.col='blue',edge.col='gray')
ani.replay()
```

Or bump it up to 30 for a slow-motion replay:

```{r,fig.keep='none',message=FALSE}
render.animation(wheel,render.par=list(tween.frames=30),
                 vertex.col='blue',edge.col='gray')
ani.replay()
```

Note that the `render.d3movie` command doesn't have a `tween.frames` argument, because it interpolates the positions in the app. It has an `animationDuration` parameter that can be passed provided and an 'animation speed' control in the app which the use can adjust using the menu on the upper left. 

If you are like me, you probably forget what the various parameters are and what they do.  You can use `?compute.animation` or `?render.animation` to display the appropriate help files. and `?plot.network` to show the list of plotting control arguments.

*****
**Question:** Why is all this necessary? Why not just call plot.network over and over at each time point?

*****


### Animated Layout Algorithms
First some background about graph layouts.  Producing layouts of dynamic networks is generally a computationally difficult problem. And the definition of what makes a layout "good" is often ambiguous or very specific to the domain of the data being visualized. The ndtv package aims for the following sometimes conflicting animation goals:

* Similar layout goals as static layouts (minimize edge crossing, vertex overlap, etc)
* Changes in network structure should be reflected in changes in the vertex positions in the layout.
* Layouts should remain as visually stable as possible over time.
* Small changes in the network structure should lead to small changes in the layouts. 

Many otherwise excellent static layout algorithms often don't meet the last two goals well, or they may require very specific parameter settings to improve the stability of their results for animation applications. 

So far, in ndtv we are using variations of Multidimensional Scaling (MDS) layouts.  MDS algorithms use various numerical optimization techniques to find a configuration of points (the vertices) in a low dimensional space (the screen) where the distances between the points are as close as possible to the desired distances (the edges). This is somewhat analogous to the process of squashing a 3D world globe onto a 2D map: there are many useful ways of doing the projection, but each introduces some type of distortion. For networks, we are attempting to define a high-dimensional "social space" to project down to 2D.

The `network.layout.animate.*` layouts included in `ndtv` are adaptations or wrappers for existing static layout algorithms with some appropriate parameter presets. They all accept the coordinates of the previous layout as an argument so that they can try to construct a suitably smooth sequence of node positions. Using the previous coordinates allows us to "chain" the layouts together. This means that each visualization step can often avoid some computational work by using a previous solution as its starting point, and it is likely to find a solution that is spatially similar to the previous step. 


#### Why we avoid Fruchterman-Reingold
The Fruchterman-Reingold algorithm has been one of the most popular layout algorithms for graph layouts (it is the default for `plot.network`).  For larger networks it can be tuned to run much more quickly than most MDS algorithms.  Unfortunately, its default optimization technique introduces a lot of randomness, so the "memory" of previous positions is usually erased each time the layout is run, producing very unstable layouts when used for animations. Various authors have had useful animation results by modifying FR to explicitly include references to vertices' positions in previous time points. Hopefully we will be able to include such algorithms in future releases of ndtv.

#### Kamada-Kawai adaptation
The Kamada-Kawai network layout algorithm is often described as a "force-directed" or "spring embedded" simulation, but it is mathematically equivalent to some forms of MDS (Kamada-Kawai uses Newton-Raphson optimization instead of SMACOF stress-majorization). The function `network.layout.animate.kamadakawai` is essentially a wrapper for `network.layout.kamadakawai`. It computes a symmetric geodesic distance matrix from the input network using `layout.distance` (replacing infinite values with `default.dist`), and seeds the initial coordinates for each slice with the results of the previous slice in an attempt to find solutions that are as close as possible to the previous positions. It is not as fast as MDSJ, and the layouts it produces are not as smooth. Isolates often move around for no clear reason. But it has the advantage of being written entirely in R, so it doesn't have the pesky external dependencies of MDSJ. For this reason it is the default layout algorithm. 

```{r,message=FALSE,results='hide'}
compute.animation(short.stergm.sim,animation.mode='kamadakawai')
saveVideo(render.animation(short.stergm.sim,render.cache='none',
                           main='Kamada-Kawai layout'),
          video.name='kamadakawai_layout.mp4')
```

#### MDSJ (Multidimensional Scaling for Java)

MDSJ is a very efficient implementation of "SMACOF" stress-majorization Multidimensional Scaling. The `network.layout.animate.MDSJ` layout gives the best performance of any of the algorithms tested so far -- despite the overhead of writing matrices out to a Java program and reading coordinates back in.  It also produces very smooth layouts with less of the wobbling and flipping which can sometimes occur with Kamada-Kawai. Like Kamada-Kawai, it computes a symmetric geodesic distance matrix from the input network using `layout.distance` (replacing infinite values with `default.dist`), and seeds the initial coordinates for each slice with the results of the previous slice.

As noted earlier, the MDSJ library is released under Creative Commons License "by-nc-sa" 3.0.  This means using the algorithm for commercial purposes would be a violation of the license. More information about the MDSJ library and its licensing can be found at http://www.inf.uni-konstanz.de/algo/software/mdsj/.

```{r,echo=FALSE,message=FALSE}
# the command below will default to not installing MDSJ in a non-interactive session
# so to make sure it is installed for this sweave build, call it internally
mdsj.dir <- file.path(path.package("ndtv"), "java/")
ndtv:::install.mdsj(mdsj.dir)
```

```{r,message=FALSE,results='hide'}
compute.animation(short.stergm.sim,animation.mode='MDSJ')
saveVideo(render.animation(short.stergm.sim,render.cache='none',
                           main='MDSJ layout'),
          video.name='MDSJ_layout.mp4')
```

#### Graphviz layouts

The Graphviz (Gansner and North 2000)  external layout library includes a number of excellent algorithms for graph layout, including `neato`, an stress-optimization variant, and `dot` a hierarchical layout (for trees and Directed Acyclic Graph (DAG) networks). As Graphviz is not an R package, you must first install the the software on your computer following the instructions at `?install.graphviz` before you can use the layouts. The layout uses the `export.dot` function to write out a temporary file which it then passes to Graphviz.

```{r,message=FALSE}
compute.animation(short.stergm.sim,animation.mode='Graphviz')
saveVideo(render.animation(short.stergm.sim,render.cache='none',
                           main='Graphviz-neato layout'),
          video.name='gv_neato_layout.mp4')
compute.animation(short.stergm.sim,animation.mode='Graphviz',
                  layout.par=list(gv.engine='dot'))

```

#### Existing coordinates or customized layouts
The `network.layout.animate.useAttribute` layout is useful if you already know exactly where each vertex should be drawn at each time step (based on external data such as latitude and longitude), and you just want `ndtv` to render out the network. It just needs to know the names of the dynamic TEA attribute holding the `x` coordinate and the `y` coordinate for each time step. 

The `useAttribute` layout also provides an easy way to pass in static coordinates in order to create an animation to show edge changes with static vertex positions.  This can be handy for 'flipbook'-style animations and geographic map overlays.  

```{r,eval=FALSE}
staticCoords<-network.layout.kamadakawai(short.stergm.sim,layout.par = list())
activate.vertex.attribute(short.stergm.sim,'x',staticCoords[,1],onset=-Inf,terminus=Inf)
activate.vertex.attribute(short.stergm.sim,'y',staticCoords[,2],onset=-Inf,terminus=Inf)
compute.animation(short.stergm.sim,animation.mode='useAttribute')
```



It is also possible to write your own layout function and easily plug it in by defining a function with a name like `network.layout.animate.MyLayout`.  See the `ndtv` package vignette for a circular layout example `browseVignette(package='ndtv')`.

*****
**Excercise:** Compare the algorithms by watching the video outputs or watch this side-by-side composite version: http://statnet.org/movies/layout_compare.mp4. What differences are noticeable?

*****

```{r, cache=TRUE,echo=FALSE,results='hide'}
# use ffmpeg to composite the three videos into one
system(paste('ffmpeg -i ',ani.options("outdir"),'/MDSJ_layout.mp4', ' -i  ',ani.options("outdir"),'/kamadakawai_layout.mp4',' -i  ', ani.options("outdir"),'/gv_neato_layout.mp4', ' -filter_complex "[0:v:0]pad=iw*3:ih[bg]; [bg][1:v:0]overlay=w[both]; [both][2:v:0]overlay=w*2"  ',ani.options("outdir"),'/layout_compare.mp4',sep=''))
system(paste('xdg-open ',ani.options("outdir"),'/layout_compare.mp4',sep=''))
```

More detailed information about each of the layouts and their parameters can be found on the help pages, for example `?network.layout.animate.kamadakawai`.

## Understanding how tsna works

The `tsna` package currently provides four main classes of metrics

* Traditional SNA metrics evaluated repeatedly to return a time series
* Statistics describing properties of the network over its entire observation period
* Metrics based on measuring network distances using forward reachable paths
* Measures of event sequences

The first class of metrics requires some additional detail about how we think about dividing and aggregating time. 

### Slicing and aggregating time

Most traditional "static" network metrics don't really know what to do with dynamic networks.  They need to be fed a set of relationships describing a single point in time in the network's evolution which can then be used to compute graph metrics.   A common way to apply static metrics to characterize a time-varying object is to sample it at regular intervals, taking a sequence static observations at multiple time points and using these to describe the changes over time.  

In the case of networks, we often call this this sampling process "extracting" or "slicing" --cutting through the dynamics to obtain a static snapshot.  For the network layouts we want a sequence of these snapshots to be converted into series of coordinates in Euclidean space suitable for plotting. For graph- or vertex-level SNA indicators we want a time series of numeric values. The processes of determining a set of slicing parameters appropriate for the network phenomena and data-set of interest requires careful thought and experimentation.  As mentioned before, it is somewhat similar to the questions of selecting appropriate bin sizes for histograms.

#### Slicing panel data

In both the `wheel` and `short.stergm.sim` examples, we've been implicitly slicing up time in discrete way, extracting a static network at each unit time step.

We can plot the slice bins against the timeline of edges to visualize the "observations" of the network that the rendering process is using. When the horizontal line corresponding to an edge spell crosses the vertical gray bar corresponding to a bin, the edge would be included in that network. If this was a social network survey, each slice would correspond to one data collection panel of the network.  
```{r}
timeline(short.stergm.sim,slice.par=list(start=0,end=25,interval=1,
                      aggregate.dur=1,rule='latest'),
                      plot.vertex.spells=FALSE)
```

Looking at the first slice, which extends from time zero *until* (notice the right-open interval definition!) time 1, it appears that it should have 15 edges in it.  Let's check. We can either:

Extract the network as we have seen before and count edges...
```{r}
network.edgecount(network.extract(short.stergm.sim,onset=0,terminus=1))
```
... or just count the active edges directly with a command.
```{r}
network.edgecount.active(short.stergm.sim,onset=0,terminus=1)
```

If we want to do this for each slice, we can use the `edges` statistic from `ergm`

```{r}
tErgmStats(short.stergm.sim,'edges',start = 0,end=25,time.interval=1)
```


Following the convention `statnet` uses for representing ``discrete-time`` simulation dynamics, the edge spells always have integer lengths and extend the full duration of the slice, so it wouldn't actually matter if we used a shorter `aggregate.dur`. Each slice will still intersect with the same set of edges. 

```{r}
timeline(short.stergm.sim,slice.par=list(start=0,end=25,interval=1,
                      aggregate.dur=0,rule='latest'),
                      plot.vertex.spells=FALSE)
```


However, even for some data-sets that are collected as panels, the time units many not always be integers, or the slicing parameters might need to be adjusted to the natural time units.  For example, if we use `aggregate.dur` to specify longer duration bins, some of them will intersect with more edges


```{r,warning=FALSE}
tErgmStats(short.stergm.sim,'edges',start = 0,end=25,time.interval=2, aggregate.dur=2)
```

And, as we will see later in the windsurfers example, there are situations where using longer aggregation durations can be helpful even for panel data. 

#### Slicing streaming data

Slicing up a dynamic network created from discrete panels may appear to be fairly straightforward but it is much less clear how to do it when working with continuous time or "streaming" relations where event are recorded as a single time point. How often should we slice?  Should the slices measure the state of the network at a specific instant, or aggregate over a longer time period?  The answer probably depends on what the important features to visualize are in your data-set. One of the strengths of these packages is that they make it possible to experiment with various aggregation options. In many situations we have even found it useful to let slices mostly overlap -- increment each one by a small value to help show fluid changes on a moderate timescale instead of the rapid changes happening on a fine timescale (Bender-deMoll and McFarland 2006). 

As an example, lets look at the McFarland (2001) data of streaming classroom interactions and see what happens when we chop it up in various ways. 
```{r}
data(McFarland_cls33_10_16_96)
```

Plot the time-aggregated network
```{r}
plot(cls33_10_16_96)
```

First, we can animate at the fine time scale, viewing the first half-hour of class using instantaneous slices (`aggregate.dur=0`).
```{r,message=FALSE}
slice.par<-list(start=0,end=30,interval=2.5, 
                aggregate.dur=0,rule="latest")
compute.animation(cls33_10_16_96,
                slice.par=slice.par,animation.mode='MDSJ',verbose = FALSE)
render.d3movie(cls33_10_16_96,output.mode = 'htmlWidget')
```

Notice that although the time-aggregated plot shows a fully-connected structure, in the animation most of the vertices are isolates, occasionally linked into brief pairs or stars by speech acts. You can go to http://statnet.org/movies/ndtv_vignette/cls33_10_16_96v1.mp4 to see a version of the movie output. Once again we can get an idea of what is going on by slicing up the network by using the `timeline()` function to plot the `slice.par` parameters against the vertex and edge spells. Although the vertices have spells spanning the entire time period, in this data set the edges are recorded as instantaneous "events" with no durations.  

```{r}
timeline(cls33_10_16_96,slice.par=slice.par)
```

The very thin slices (gray vertical lines) (`aggregate.dur=0`) are not intersecting many edge events (purple numbers) at once so the momentary degrees are mostly low.  We can use the `ergm`'s `meandeg` term to compute the mean degree at each of the 50 time steps
```{r,warning=FALSE}
plot(tErgmStats(cls33_10_16_96,'meandeg'),
     main='Mean degree of cls33, 1 minute aggregation')
```


The first movie may give us a good picture of the sequence of conversational turn-taking, but it is hard to see larger structures. If we aggregate over a longer time period of 2.5 minutes we start to see the individual acts form into triads and groups. See http://statnet.org/movies/ndtv_vignette/cls33_10_16_96v2.mp4 for a version of the corresponding movie. 

```{r,message=FALSE}
slice.par<-list(start=0,end=30,interval=2.5, 
                aggregate.dur=2.5,rule="latest")
compute.animation(cls33_10_16_96,
                slice.par=slice.par,animation.mode='MDSJ',verbose=FALSE)
render.d3movie(cls33_10_16_96,
                 displaylabels=FALSE,output.mode='htmlWidget')
```

```{r}
timeline(cls33_10_16_96,slice.par=slice.par)
```

```{r,warning=FALSE}
plot(tErgmStats(cls33_10_16_96,'meandeg',
                time.interval = 2.5,aggregate.dur=2.5),
     main='Mean degree of cls33, 2.5 minute aggregation')
```

To reveal slower structural patterns we can make the aggregation period even longer, and let the slices overlap (by making `interval` less than `aggregate.dur`) so that the same edge may appear in sequential slices and the changes will be less dramatic between successive views. See http://statnet.org/movies/ndtv_vignette/cls33_10_16_96v3.mp4 for the corresponding movie.


```{r, message=FALSE}
slice.par<-list(start=0,end=30,interval=1, 
                aggregate.dur=5,rule="latest")
timeline(cls33_10_16_96,slice.par=slice.par)
compute.animation(cls33_10_16_96,
                slice.par=slice.par,animation.mode='MDSJ',verbose=FALSE)
render.d3movie(cls33_10_16_96,
                 displaylabels=FALSE,
               output.mode = 'htmlWidget')
```

```{r,warning=FALSE}
plot(tErgmStats(cls33_10_16_96,'meandeg',
                time.interval = 1,aggregate.dur=5,rule='latest'),
     main='Mean degree of cls33, overlapping 5 minute aggregation')
```

*****
**Question:** How would measurements of a network's structural properties (transitivity, betweenness, etc.) at each time point likely differ in each of the aggregation scenarios?

*****

*****
**Question:** When we use a long duration slice, for some networks it is quite likely that the edge between a pair of vertices has more than one active period. How should this condition be handled? If the edge has attributes, which ones should be shown? 

*****

Ideally we might want to aggregate the edges in some way, summing their activity durations or perhaps adding the weights together. Currently edge attributes are not aggregated and the `rule` element of the `slice.par` argument controls whether the `earliest` or `latest` attribute value should be returned for an edge when multiple elements are encountered.  

### The `ergm` and `sna` function wrappers

We've already seen several examples using the `tSnaStats` and `tErgmStats` functions.  These tools use the network statistics capabilities of the `sna` metrics and `ergm` terms  while handling the dirty work of chopping the `networkDynamic` object up into a series of appropriate `network`s (using `collapse.network`), interpreting some of the control parameters (directedness, etc), calculating the metric for each slice, and returning the results as time series (`ts`) object.  Be forewarned, this process is usually neither fast or memory efficient!  The binning of the networks is defined by the `time.interval` and `aggregate.dur` parameters, controlling the interval of time between the beginning of the bins and the duration of time that each bin aggregates. 

*****
**Exercise:** Define slicing parameters and compute a time series of graph `triad.census` values the first 20 minutes of classroom interactions using 5 minute non-overlapping slices 

```{r,warning=FALSE}
tSnaStats(cls33_10_16_96,'triad.census',
          start=0,
          end = 20,
          time.interval = 5, 
          aggregate.dur = 5)
```

*****

Notice that, unlike the previous temporal stats examples, the `triad.census` function returns multiple statistics -- the counts for each triad type -- and so `tSnaStats` returns a multivariate time series object in which each row is a time point and each column is one of the count statistics.

### Sequence measures

So far there is only one, `pShiftCount` which provides a wrapper for the implementation of Gibson's (2003) "participation shift" metric, provided by the `relevent` package (Butts, 2008). This measure considers the network to be an ordered sequence of events -- in which the exact timing is not important -- and tallies up instances of two-event exchanges into the thirteen categories Gibson used to classify conversational turn taking. 

For example, two edges in sequence, ‘i’ talks to ‘j’, and then ‘j’ responds to ‘i’, is counted as one type of event, where ‘i’ talks to ‘j’ and then ‘j’ talks to ‘k’ would be another type of event. The set of events Gibson was interested in is certainly not an exhaustive list of potential sequences, but may still be an interesting approach for characterizing dynamic networks.

If we apply the metric to the entire time period of the McFarland classroom speech acts

```{r}
pShiftCount(cls33_10_16_96)
```

We see lots of "turn-receiving" alternation (type AB-BA) and a fair amount of "turn-usurping" exchanges -- perhaps indicating time periods when multiple conversations are happening at the same time. 


Gibson's typology assumes that edges/ties directed "at the group" are distinguishable those directed to individuals, and has a strong assumption of sequential non-simultaneous events. Because the networkDynamic object does not explicitly code for 'group' utterances, simultaneous edges originating from a speaker (same onset, terminus, and tail vertex) are assumed to be directed at the group, even if not all group members are reached by the ties.

*****
**Question:** What are some key distinctions between the types of structures counted by `pShiftCount` when compared with a `triad.census`?

*****

### Durations and counts of ties

When we have access to longer duration longitudinal network data sets, it begins to be possible to examine networks in terms of temporal characterizations of edge activity without first chopping them up into bins.  For example, what are the average durations of edge activity?

The `edgeDuration` function provides a convenient way to access the information.

```{r}
edgeDuration(short.stergm.sim)
```
By default, it returns a vector of durations corresponding to each edge observed in the network. We can use standard R tools to look at these distributions. 

```{r}
summary( edgeDuration(short.stergm.sim) )
```

If we are working with event data such as the McFarland classrooms, this function at first appears less useful:

```{r}
edgeDuration(cls33_10_16_96)
```

Fortunately, there is an argument appropriate for working networks having zero-duration ties: instead of summing the duration of edges' activity spells, we tell it to just count the number of times they are active. 

```{r}
edgeDuration(cls33_10_16_96,mode='counts')
```

An important point of detail: when we compute statistics and the level of an 'edge', we are usually summing together all of the activity spells associated with that edge. Setting `subject = 'spells'` will return a duration for each edge activity spell, which is probably more consistent with what statistical models such as `tergm` consider the duration of an `edge`. For multiplex networks, setting `subject = 'dyads'` will aggregate across multiple edges linking a pair of vertices.  

```{r}
hist(edgeDuration(short.stergm.sim))  
hist(edgeDuration(short.stergm.sim,subject = 'spells')) 
```

****
**Question:** What happens to the measured durations as the observation window gets shorter? Why?

```{r}
summary(edgeDuration(short.stergm.sim))
summary(edgeDuration(short.stergm.sim,start=0,end=10))
```

****

Edge durations can tell us the relative rates at which individual relationships are active, but what if we want to know how active the vertices are across their relationships?  The `tiedDuration` function provides a vertex-level aggregation of the amount of time each vertex is "in a relationship".

```{r}
tiedDuration(short.stergm.sim)
```

****
**Question:** What might be an expected relationship between the `tiedDuration` and the `degree` of each vertex in a dynamic network?

****


### Forward path metrics
In static networks we frequently measure distances using the shortest path geodesic.  In dynamic networks that are models of possible transmission routes, we need to consider the sequence of edge timing when computing allowable 'journeys' through the network. The `tPath` function provides a way to calculate the set of temporally reachable vertices from a given source vertex starting at a specific time. 

```{r}
path<-tPath(short.stergm.sim,v = 13,
            graph.step.time=1)
path
```

By default, it does this by computing the `earliest forward reachable path`, so it also returns the earliest times each of the vertices becomes reachable in the `$tdist` component of the list, with `Inf` if it was unreachable.  The  `$previous` component gives, for each vertex, the id of the vertex it was reached by.  `$gsteps` gives the number of steps in the earliest forward path journey to reach each vertex. Note that this __is usually not the same thing as the length of the shortest time-respecting path!__ 

We showed previously that we plot the tPath overlayed on the aggregate network with `plotPaths`, but this is probably only useful when the aggregate network is not too dense. So another option is to just plot the tree of the reachable path as if it was a network. By default this will label the edges with the times that the path crossed them. 

```{r}
plot(path,edge.lwd = 2)
```

The `transmissionTimeline` is an alternate view which is often helpful for debugging and understanding tPaths. It plots the time at which each vertex was reached against the number of steps in the path with lines corresponding to the edges that the path crossed.

```{r}
transmissionTimeline(path,jitter=TRUE,
          main='Earliest forward path from vertex 13')
```

****
**Question:** Are reachable paths symmetric in an undirected network? If vertex `i` can reach `j`, can we assume that `j` can reach `i`?

****

Because reachable paths are not symmetric, the idea of "components" is much more complex in dynamic networks.  However, we can use the reachable paths to find the sizes of the 'forward reachable sets' from each vertex in the network with the `tReach` function.  This corresponds to the distribution of maximal possible epidemic sizes for a trivial SI infection model with a transmission probability of 1.0, so may give us a possible measure of how effective the network might be at transmitting. 

If we compute this for the `short.stergm.sim`, we will get back a vector where each element holds the reachable set size of the corresponding vertex -- starting from the beginning of the observation period.

```{r}
tReach(short.stergm.sim)
```

This tells us that the example network is fairly well temporally connected.  Most of the vertices can eventually reach at least 11 other vertices within the period of time we have "observed". For a network this small, we can efficiently compute all of the paths.  But for larger networks we might want to just get a sense of the distribution of forward set sizes using the `sample` argument to only compute paths from a subset of seed vertices. 


# Using the tools effectively
Some additional tips, tricks, and helpful information for temporal visualization.

## Animation output formats for ndtv
In this tutorial we have been only playing back animations in the R plot window. But what if you want to share your animations with collaborators or post them on the web? Assuming that the external dependencies are correctly installed, we can save out animations in multiple useful formats supported by the `ndtv` and the `animation` package:

* `render.d3movie()` plays an HTML5 vector graphics version of the animation in a browser window, Rmarkdown, or optionally saves it for later embedding.
* `ani.replay()` plays the animation back in the R plot window. (see `?ani.options` for more parameters)
* `saveVideo()` saves the animation as a video file on disk (if the FFmpeg library is installed).
* `saveGIF()` creates an animated GIF (if ImageMagick's  `convert` is installed)
* `saveLatex()` creates an animation embedded in a PDF document

See the help page for each function for detailed listing of parameters. We will quickly demonstrate some useful options below.

### HTML5 / SVG video files

As we saw earlier, `ndtv` includes the `render.d3movie` that, instead of using R's plotting functions and the animation library, embeds the animation information into a web page along with "ndtv-d3 player" as an interactive HTML5 SVG animation for display in a modern web browser.


```{r,message=FALSE}
render.d3movie(wheel,vertex.col='blue', edge.col='gray')
```

The `render.d3movie` supports most (but not all) of the same commonly used plot arguments as `render.animation`. For a list of exactly which arguments, see `?render.d3Movie`.  There are also some additional arguments that can be used to configure HTML styling and interaction properties such as tool-tips. 

We've provided a tutorial devoted just to the ndtv-d3 features available at http://statnet.org/workshops/SUNBELT/current/ndtv/ndtv-d3_vignette.html  It demonstrates great features such as embedding animations in Rmarkdown documents (Allaire, et. al. 2015) such as this tutorial, and some of the features that may be useful for building Shiny apps. 


### Video files
Since we just rendered the "wheel" example movie, it is already cached and we can capture the output of `ani.replay()` into a movie file. Try out the various output options below.

#### Saving video
Save out an animation, providing a non-default file name for the video file:

```{r,message=FALSE}
saveVideo(ani.replay(),video.name="wheel_movie.mp4")
```

You will probably see a lot output on the console from ffmpeg reporting its status, and then it should open the movie in an appropriate viewer on your machine.

#### Changing video size
Sometimes we may want to change the pixel dimensions of the movie output to make the plot (and the file size) much larger.
```{r,message=FALSE}
saveVideo(ani.replay(),video.name="wheel_movie.mp4",
          ani.width=800,ani.height=800)
```

#### Adjusting video quality
We can increase the video's image quality (and file size) by telling ffmpeg to use a higher bit-rate (less compression) for the video.

```{r,message=FALSE}
saveVideo(ani.replay(),video.name="wheel_movie.mp4",
          other.opts="-b:v 5000k")
```

#### Rendering video directly to disk
Because the `ani.record()` and `ani.replay()` functions cache each plot image in memory, they are not very speedy and the rendering process will tend to slow to a crawl down as memory fills up when rendering large networks or long movies.  We can avoid this by saving the output of `render.animation` directly to disk by wrapping it inside the `saveVideo()` call and setting `render.cache='none'`.
```{r,message=FALSE}
saveVideo(render.animation(wheel,vertex.col='blue',
          edge.col='gray',render.cache='none'),
          video.name="wheel_movie.mp4")
```

### Animated GIF files
We can also export an animation as an animated GIF image. GIF animations will be very large files, but are very portable for sharing on the web. To render a GIF file, you must have ImageMagick installed. See `?saveGIF` for more details. 

```{r,message=FALSE,results='none'}
saveGIF(render.animation(wheel,vertex.col='blue',
          edge.col='gray',render.cache='none'),
         movie.name="wheel_movie.gif")
```

### Animated PDF/Latex files
The `animation` package supports including animations inside PDF documents if you have the appropriate Latex utilities installed. However, the animations will only play inside Adobe Acrobat PDF viewers so it is probably less portable than using GIF or video renders.

```{r,message=FALSE}
saveLatex(render.animation(wheel,vertex.col='blue',
          edge.col='gray',render.cache='none'))
```



*****
**Exercise:** Using the list of options from the help page `?ani.options`, locate the option to control the time delay interval of the animation, and use it to render a video where each frame stays on screen for 2 seconds.

```{r,message=FALSE,results='hide'}
saveVideo(render.animation(wheel,vertex.col='blue',
          edge.col='gray',render.cache='none',
          render.par=list(tween.frames=1),
          ani.options=list(interval=2)),
         video.name="wheel_movie.mp4")
```

*****

*****
**Exercise:** Using the list of options from the help page `?render.d3movie`, locate the option to control the title and background color and load an animation in the web browser with the `d3.options` set so that it will play automatically, with a much faster duration than normal.

```{r,message=FALSE,results='hide'}
render.d3movie(wheel,vertex.col='blue',
          main="I'm a wheel!",
          bg='gray',
          d3.options=list(animationDuration=100,animateOnLoad=TRUE))
          
```

*****

*****
**Question:** What are some trade-offs between the HTML5 and video approaches to saving and sharing network animations?

****

## Vertex dynamics
In some dynamic network data the vertices may also enter or leave the network (become active or inactive, birth/death).  Lin Freeman's windsurfer social interaction data-set (Almquist and Butts 2011) is a good example of this. Vertices enter and exit frequently because different sets of people are present on the beach on successive days. For instance, look at vertex 74 in contrast to vertex 1 on the timeline plot.

```{r}
data(windsurfers)
timeline(windsurfers,plot.edge.spells=FALSE)
```


```{r,message=FALSE}

slice.par<-list(start=1,end=31,interval=1, 
                aggregate.dur=1,rule="earliest")
windsurfers<-compute.animation(windsurfers,slice.par=slice.par,
                               default.dist=3,
                               animation.mode='MDSJ',
                               verbose=FALSE)

render.d3movie(windsurfers,vertex.col="group1",
                 edge.col="darkgray",
                 displaylabels=TRUE,label.cex=.6,
                 label.col="blue", verbose=FALSE,
               main='Windsurfer interactions, 1-day aggregation',
               output.mode = 'htmlWidget')

```

These networks also have a lot of isolates, which tends to scrunch up the rest of the components in the network plot so they are hard to see.  Setting the lower `default.dist` above can help with this. In this example (see http://statnet.org/movies/ndtv_vignette/windsurfers_v1.mp4) the turnover of people on the beach is so rapid that structure appears to change chaotically, and it is quite hard to see what is going on. Notice the blank period at day 25 where the network data is missing.

We can still calculate some vertex-level metrics, such as the activity durations for each vertex. 

```{r}
hist( vertexDuration(windsurfers) )
```

Not surprisingly, most of the windsurfers spend less than 5 days a month on the beach. 

*****
**Question:**  What is the difference between calculating the vertex durations with `subject='vertices'` and `subject='spells'`? 

*****

What is happening to the density of the network as vertices enter and exit? Should we be thinking of the vertices as inactive, or unobserved?

```{r}
par(mfcol=c(3,1))
# an example of a 'roll-your-own' networkDynamic statistic
netSizes<-sapply(1:32,function(t){ network.size.active(windsurfers,at=t) })
plot( 1:32,netSizes ,type='l', 
      main = 'Number of windsurfers active each day')

plot( tErgmStats(windsurfers,'edges') ,
      main = 'Number of widsurfer interaction edges active each day')

plot( tSnaStats(windsurfers, 'gden') , 
      main = 'Graph density of winsurfer interaction edges each day')
par(mfcol=c(1,1))
```



There is also a lot of periodicity, since many more people go to the beach on weekends. So in this case, lets try a week-long slice by setting `aggregate.dur=7` to try to smooth it out so we can see changes against the aggregate weekly structure. 

```{r,message=FALSE}
slice.par<-list(start=0,end=24,interval=1, 
                aggregate.dur=7,rule="earliest")
windsurfers<-compute.animation(windsurfers,slice.par=slice.par,
                               default.dist=3,
                               animation.mode='MDSJ',
                               verbose=FALSE)
render.d3movie(windsurfers,vertex.col="group1",
                 edge.col="darkgray",
                 displaylabels=TRUE,label.cex=.6,
                 label.col="blue", verbose=FALSE,
               main='Windsurfer interactions, 7-day aggregation',
               output.mode = 'htmlWidget')
```

This new rolling--"who interacted this week" network (see http://statnet.org/movies/ndtv_vignette/windsurfers_v2.mp4) is larger and more dense (which is to be expected) and also far more stable. We see new ties forming against a background of pre-existing ties.  There is still some turnover due to people who don't make it to the beach every week but it is now possible to see some of the sub-groups of 'regulars' and the the various bridging individuals.

*****
**Question:**  Why did we adjust the ending time parameter?

*****

*****
**Question:** How would a researcher determine the "correct" aggregation period or data collection interval for a dynamic process? When the "same" network is sampled repeatedly, how can we distinguish sampling noise from network dynamics?

*****


## Dynamic network attributes
Vertices and edges are not the only things that change over time, how do we display dynamic attributes (such as infection status) and changes to structural properties of the network?

If a network has dynamic attributes defined, they can be used to define graphic properties of the network which change over time.  We can activate some attributes on our earlier "wheel" example, setting a dynamic attribute for edge widths. The help file listing and explaining dynamic TEA attributes can be displayed with `?dynamic.attributes`.

We can attach an attribute named `width` to the edges which will take values of 1, 5, and 10 for various ranges of times. 
```{r}
activate.edge.attribute(wheel,'width',1,onset=0,terminus=3) 
activate.edge.attribute(wheel,'width',5,onset=3,terminus=7)
activate.edge.attribute(wheel,'width',10,onset=7,terminus=Inf)
```

And check what we created.

```{r}
list.edge.attributes(wheel)
get.edge.attribute.active(wheel,'width', at=2)
get.edge.attribute.active(wheel,'width', onset=5,terminus=6)
get.edge.attribute.active(wheel,'width', at=300)
```

There are many features and complexities that come up when working with dynamic attributes.  For example, with the commands above, we've defined values for edges even when those edges are inactive.  Compare:

```{r}
get.edge.attribute.active(wheel,'width', at=2)
get.edge.attribute.active(wheel,'width', at=2,require.active=TRUE)
```

When using an attribute to control a plot parameter we must make sure the attributes are always defined for every time period that the network will be plotted or else an error will occur. So it is often good practice first set a default value from `-Inf` to `Inf`  before overwriting with later commands defining which elements we wanted to take a special value. 

```{r}
activate.vertex.attribute(wheel,'mySize',1, onset=-Inf,terminus=Inf)
activate.vertex.attribute(wheel,'mySize',3, onset=5,terminus=10,v=4:8)
```

We can set values for vertex colors.
```{r}
activate.vertex.attribute(wheel,'color','gray',onset=-Inf,terminus=Inf)
activate.vertex.attribute(wheel,'color','red',onset=5,terminus=6,v=4)
activate.vertex.attribute(wheel,'color','green',onset=6,terminus=7,v=5)
activate.vertex.attribute(wheel,'color','blue',onset=7,terminus=8,v=6)
activate.vertex.attribute(wheel,'color','pink',onset=8,terminus=9,v=7)
```

There are also query functions for TEAs which we can use to ask when an attribute takes a specific value or matches a criteria

```{r}
when.vertex.attrs.match(wheel,'color',value = 'green')
when.edge.attrs.match(wheel,'width', match.op = '>', value = 3)
```

### Controlling plot properties using dynamic attributes (TEAs)

Finally we render it, giving the names of the dynamic attributes to be used to control the plotting parameters for edge with, vertex size, and vertex color. 

```{r,fig.keep='none'}
render.animation(wheel,edge.lwd='width',vertex.cex='mySize',
                 vertex.col='color',verbose=FALSE)
ani.replay()
```

The attribute values for the time points are defined using `rule` argument to `network.collapse`, which controls the behavior if multiple values are active for the plot period. 


*****
**Exercise:** Using the wheel network, create a dynamic vertex attributed named "group".  Define the TEA so that initially most of the vertices will be in group "A", but over time more and more will be in group "B" 

*****

### Controlling plot properties with special functions

Sometimes it is awkward or inefficient to pre-generate dynamic attribute values.  Why create and attach another attribute for color if it is just a simple transformation of an existing attribute or measure? We can define a function to transform the observed network values into an appropriate plotting attribute. Recall that R allows us to define new functions whenever we want. For example, we could define `myFunction()`  that will accept `myArgument`, transform it, and return the new value.

```{r}
myFunction<-function(myArgument){
  # do things with myArgument  
  myArgument<-myArgument+1
  # return the result of the function
  return(myArgument)
}

myFunction(1)
```

The `render.animation` function has the ability to accept the `plot.network` arguments as R functions.  These functions will be evaluated "on the fly" at each time point as the network is rendered and can operate on the attributes and properties of the collapsed network. 

For example, if we wanted to use our previously created `'width'` attribute to control the color of edges along with their width, we could define a function to extract the value of the `'width'` edge attribute from the momentary slice network and map it to the red component of an RGB color.  We can render the network, setting `edge.col` equal to this function. 

```{r,fig.keep='none'}
render.animation(wheel,edge.lwd=3, 
    edge.col=function(slice){rgb(slice%e%'width'/10,0,0)},
    verbose=FALSE)
ani.replay()
```

Notice the `slice` function argument and the use of `slice` instead of the original name of the network in the body of the function. The arguments of plot control functions must draw from a specific set of named arguments which will be substituted in and evaluated at each time point before plotting.  The set of valid argument names that can be used in special functions is:

  * `net` is the original (un-collapsed) network
  * `slice` is the static network slice to be rendered, collapsed with the appropriate onset and terminus
  * `s` is the slice number in the sequence to be rendered
  * `onset` is the onset (start time) of the slice to be rendered
  * `terminus` is the terminus (end time) of the slice to be rendered

We can also define functions based on calculated network measures such as betweenness rather than network attributes: 

```{r,fig.keep='none'}
require(sna) # load library of SNA measures
wheel%n%'slice.par'<-list(start=1,end=10,interval=1, 
                          aggregate.dur=1,rule='latest')
render.animation(wheel,
      vertex.cex=function(slice){(betweenness(slice)+1)/5},
      verbose=FALSE)
ani.replay()
```

Notice that in this example we had to modify the start time using the `slice.par` setting to avoid time 0 because the `betweenness` function in the `sna` package will give an error for a network with no edges.  

*****
**Exercise:** Write a functional plot argument that scales vertex size in proportion to momentary degree

*****

The main plot commands accept functions as well, so it is possible to do fun things like implement a crude zoom effect by setting `xlim` and `ylim` parameters to be dependent on the time. 

```{r,fig.keep='none'}
render.animation(wheel,
      xlim=function(onset){c(-5/(onset*0.5),5/(onset*0.5))},
      ylim=function(onset){c(-5/(onset*0.5),5/(onset*0.5))},
      verbose=FALSE)
ani.replay()
```

### Pre-written "special effects" functions
The package also includes some pre-written ``special effects'' functions that can be used for common plotting tasks, such as coloring edges by their age.  For example, we can have an animation where edges start out red and fade to green as they age. 

```{r,fig.keep='none'}
render.animation(wheel,
      edge.col=effectFun('edgeAgeColor',fade.dur=5,
                      start.color='red',end.color='green'),
      edge.lwd=4,
      verbose=FALSE)
ani.replay()
```

The `effectFun` function looks for functions named `effect.xxx`, substitutes in any matching arguments, and returns a un-evaluated function that can be passed into a render as functional plot argument. 

These functions can be used for static plots as well.  For this you can call the effect directly (`effect.edgeAgeColor()` instead of `effectFun('edgeAgeColor')`)

```{r}
plot(wheel,edge.col=effect.edgeAgeColor(wheel,onset=10,fade.dur=10,
                      start.color='red',end.color='green'),
      edge.label=edges.age.at(wheel,at=10),
      edge.lwd=8)
```

## Using and aggregating edge weights and counts
In the previous examples we have treated the networks we are visualizing as un-weighted. But for some applications it may be useful to incorporate edge weight information in a layout. Even if the original network data does not contain weights, we may wish to perform operations using edge duration information. For example, when we are rendering an aggregate network, should an edge that exists for a single moment be treated the same way as an edge that exists the entire time?  

By default, the `collapse.network()` function returns an ordinary static network.  But setting the argument `rm.time.info=FALSE` will cause it to add some attributes with crude summary information about the activity of the edges and vertices over the time period of aggregation. (We could of course define our own more sophisticated aggregation functions, see later examples.)

```{r}
simAgg <-network.collapse(short.stergm.sim,rm.time.info=FALSE,
                          rule='latest')
list.edge.attributes(simAgg)
```

Notice the `activity.count` and `activity.duration` that are now attached to the edges.  

By default the layout algorithms will assume that all edges should have the same "ideal" length, any weights or values attached to the edge will be ignored. But if we do have edge values, either from raw data or by aggregating the edges over time, we might want to have the layout attempt to map that information the desired lengths of the edges.  The `weight.attr` argument makes it possible to pass in the name of a numeric edge attribute to be used in constructing the `layout.dist` matrix of desired distances between vertices. 

Lets plot the aggregate network with edge weights ignored.  But instead of using the normal `plot.network` command alone, we are going to extract the coordinates created by `compute.animation` and feed them into the plot (this is just for constructing the examples, no need to do this for real movies). We will also use the `activity.duration` attribute to control the drawing width and labels for the edges.

```{r,results='hide',message=FALSE}
# set slice par to single slice for entire range
slice.par<-list(start=0,end=25,interval=25, 
                aggregate.dur=25,rule='latest')
compute.animation(short.stergm.sim,animation.mode='MDSJ',
                  slice.par=slice.par)
# extract the coords so we can do a static plot
coords<-cbind(get.vertex.attribute.active(short.stergm.sim, 
                                          'animation.x',at=0),
              get.vertex.attribute.active(short.stergm.sim, 
                                          'animation.y',at=0))
plot(simAgg,coord=coords,
     edge.lwd='activity.duration', edge.col='#00000055',
     edge.label='activity.duration',edge.label.col='blue',
     edge.label.cex=0.5,main='Edge weights ignored')
```

For comparison, we will compute the layout so that the higher-valued edges draw vertices closer together (the default `weight.dist=FALSE` considers edge weights to be similarities)
```{r,results='hide',message=FALSE}
compute.animation(short.stergm.sim,weight.attr='activity.duration',
          animation.mode='MDSJ',seed.coords=coords,default.dist=20)
coords<-cbind(get.vertex.attribute.active(short.stergm.sim, 
                                          'animation.x',at=0),
              get.vertex.attribute.active(short.stergm.sim, 
                                          'animation.y',at=0))
plot(simAgg,coord=coords,
     edge.lwd='activity.duration', edge.col='#00000055',
     edge.label='activity.duration',edge.label.col='blue',
     edge.label.cex=0.5,main='Edge weights as similarity')
```

Now compute layout with `weight.dist=TRUE` so weights are treated as distance and higher-valued edges push vertices further apart.
```{r,results='hide',message=FALSE}
compute.animation(short.stergm.sim,weight.attr='activity.duration',
                  weight.dist=TRUE, animation.mode='MDSJ',
                  seed.coords=coords,default.dist=20)
coords<-cbind(
  get.vertex.attribute.active(short.stergm.sim, 'animation.x',at=0),
  get.vertex.attribute.active(short.stergm.sim, 'animation.y',at=0)
)
plot(simAgg,coord=coords,
     edge.lwd='activity.duration', edge.col='#00000055',
     edge.label='activity.duration',edge.label.col='blue',
     edge.label.cex=0.5,main='Edge weights as distance')
```

Although we can clearly see that the layout is trying to do what we ask it, the result is a graph that is visually hard to read.  Part of the problem is that we are asking the layout to achieve something difficult: the edge weights (and corresponding desired lengths) differ by more than an order of magnitude.
```{r}
range(simAgg%e%'activity.duration')
range(log(simAgg%e%'activity.duration'+1))
```

This suggests a solution of attaching a new edge attribute containing the logged duration, and using that as the `weight.attr`
```{r,message=FALSE}
set.edge.attribute(short.stergm.sim,'logDuration',
                   log(simAgg%e%'activity.duration'+1))
compute.animation(short.stergm.sim,
              weight.attr='logDuration',
                  animation.mode='MDSJ',seed.coords=coords)
coords<-cbind(
  get.vertex.attribute.active(short.stergm.sim, 'animation.x',at=0),
  get.vertex.attribute.active(short.stergm.sim, 'animation.y',at=0))
plot(simAgg,coord=coords,
     edge.lwd='activity.duration', edge.col='#00000055',
     edge.label='activity.duration',edge.label.col='blue',
     edge.label.cex=0.5,main='Edge weights as log similarity')
```

This gives us something better looking -- big edges are a bit shorter, but not so much that they squinch up the layout.

*****
**Question:** What types of data have edge weights that would best be thought of as distances? Similarities?

*****

## Adjusting spacing of isolates and components
We've briefly mentioned the `default.dist` parameter earlier. Most of the layouts use the `layout.dist` function to compute a matrix of geodesic path distances between vertices. Because there isn't a way to compute a path distance between vertices that have no connections (or between disconnected components) the empty cells of the matrix are filled in with a default value provided by `default.dist`. This value can be tweaked to increase or decrease the spacing between isolates and disconnected components. However, because this works by essentially introducing invisible edges between all of the elements, it can also introduce some distortion in the layout. The default value for `default.dist` is `sqrt(network.size(net))`, see `?layout.dist` for more information. 

To demonstrate this we will work with a single static slice of the network and call the animation layout directly so we can avoid rendering out the entire movie for each test. 

```{r,results='hide',cache=TRUE}
data(msm.sim)
msmAt50<-network.extract(msm.sim,at=50)
network.size(msmAt50)
plot(msmAt50,coord=network.layout.animate.MDSJ(msmAt50),vertex.cex=0.5)
```

In this case, the default distance must have been set to about 31 (square root of 1000). This results in the giant component being well separated from the smaller components and isolates. Although this certainly focuses visual attention nicely on the big component, it squishes up the rest of the network.  We can try setting the value lower.

```{r,results='hide',cache=TRUE}
plot(msmAt50,coord=network.layout.animate.MDSJ(msmAt50,default.dist=10),
     vertex.cex=0.5)
```

But then the `default.dist` value was too small to effectively separate the components, resulting in a lot of unnecessary edge crossing. So lets try an intermediate value.

```{r,results='hide',cache=TRUE}
plot(msmAt50,coord=network.layout.animate.MDSJ(msmAt50,default.dist=18),
     vertex.cex=0.5)
```

For this network, `default.dist=18` seems to give a reasonable compromise between spacing and scaling, but it can still lead to some edge overlaps.  We can now compute the overall movie to see how it works at various points in time.   And then peek at four time points to see if the parameter is going to give reasonable values over the time range of the movie. 

```{r,results='hide',message=FALSE,cache=TRUE}
# calculating for this network size will be slow
# expect this command to take up to 5 minutes
compute.animation(msm.sim,animation.mode='MDSJ',default.dist=18)
filmstrip(msm.sim,frames=4,displaylabels=FALSE,vertex.cex=0.5)
```

So it seems like it will work acceptably, but by the end of the movie the giant component will have grown enough to start squishing the rest of the network. 

# Importing data and constructing networkDynamic objects

## Constructing a movie from external data in matrix form
At this point you might be thinking: "All of this dynamic stuff is well and good, but my data were collected in panels and stored as matrices. Can I still make a network animation?"

The answer is yes! We will use the example Harry Potter Support Networks of Goele Bossaert and Nadine Meidert (2013). They have coded the peer support ties between 64 characters appearing in the text of each of the well-known fictional J. K. Rowling novels and made the data available for general use in the form of 6 text formatted adjacency matrices and several attribute files.  You can download and unzip the data files from http://www.stats.ox.ac.uk/~snijders/siena/HarryPotterData.html, or use the R code below to load in directly from the zip file.  The dataset is also included along with a number of other interesting examples in the `networkDynamic` object in the `networkDynamicData` (Bender-deMoll 2014) package.

```{r}
# tmp filename for the data
webLoc<-"http://www.stats.ox.ac.uk/~snijders/siena/bossaert_meidert_harrypotter.zip"
temp_hp.zip <- tempfile() 
download.file(webLoc,temp_hp.zip)
# read in first matrix file, unziping in the process
hp1 <- read.table(unz(temp_hp.zip, "hpbook1.txt"), 
                  sep=" ",stringsAsFactors=FALSE)
```

Notice the `stringsAsFactors=FALSE` argument to `read.table`. This prevents the strings from being converted into factors, which then may unexpectedly appear as integers causing all kinds of headaches. Now we should confirm that the data have the shape we expect.  Since there are 64 characters, we expect a 64x64 matrix. 
```{r}
dim(hp1)
# peek at "upper-left" corner of file
hp1[1:12,1:12]
```

And lets try quickly converting to a network static and plotting to make sure it works. 
```{r}
plot(as.network(hp1))
```

Since that seems to work, lets load in the rest of the files. 
```{r}
# tmp filename for the data
hp2 <- read.table(unz(temp_hp.zip, "hpbook2.txt"), 
                  sep=" ",stringsAsFactors=FALSE)
hp3 <- read.table(unz(temp_hp.zip, "hpbook3.txt"), 
                  sep=" ",stringsAsFactors=FALSE)
hp4 <- read.table(unz(temp_hp.zip, "hpbook4.txt"), 
                  sep=" ",stringsAsFactors=FALSE)
hp5 <- read.table(unz(temp_hp.zip, "hpbook5.txt"), 
                  sep=" ",stringsAsFactors=FALSE)
hp6 <- read.table(unz(temp_hp.zip, "hpbook6.txt"), 
                  sep=" ",stringsAsFactors=FALSE)
```

To construct a `networkDynamic` object, we will arrange them in a list and then convert it with the `networkDynamic()` utility function.
```{r}
hpList<-list(hp1,hp2,hp3,hp4,hp5,hp6)
# convert adjacency matrices to networks
hpList<-lapply(hpList,as.network.matrix,matrix.type='adjacency')
# convert list of networks to networkDynamic
harry_potter_support<-networkDynamic(network.list=hpList)
```

Next we will read in the names from the auxiliary file and attach them to the network as vertex names.
```{r}
# read in and assign the names
names<-read.table(unz(temp_hp.zip, "hpnames.txt"),
                  sep="\t",stringsAsFactors=FALSE,header=TRUE)
network.vertex.names(harry_potter_support)<-names$name
```

And similarly for the other attributes.
```{r}
# read in and assign the attributes
attributes<-read.table(unz(temp_hp.zip, "hpattributes.txt"),
                       sep="\t",stringsAsFactors=FALSE,header=TRUE)
harry_potter_support%v%'id'<-attributes$id
harry_potter_support%v%'schoolyear'<-attributes$schoolyear
harry_potter_support%v%'gender'<-attributes$gender
harry_potter_support%v%'house'<-attributes$house
```

As a courtesy to other users (or our future selves) we will add a special `net.obs.period` attribute to provide some meta data about the temporal model for this dataset.  See `?net.obs.period` for more information. 
```{r}
harry_potter_support%n%'net.obs.period'<-list(
  observations=list(c(0,6)),
  mode="discrete", 
  time.increment=1,
  time.unit="book volume")
```

Now for the important question: which vertex is Harry Potter?

```{r}
which(network.vertex.names(harry_potter_support)=="Harry James Potter")
```

When we render out the movie it is going to look like *Harry Potter and the Philosopher's Stone*, right?

```{r,fig.keep='none',results='hide',message=FALSE}
render.animation(harry_potter_support)
```

Lets tweak it a bit for some more refinement
```{r,message=FALSE}
compute.animation(harry_potter_support,
                  animation.mode='MDSJ',
                  default.dist=2,
                  verbose=FALSE)
render.d3movie(harry_potter_support,
            render.par=list(tween.frames=20),
            vertex.cex=0.8,label.cex=0.8,label.col='gray',
            # make shape relate to school year
            vertex.sides=harry_potter_support%v%'schoolyear'-1983,
            # color by gender
            vertex.col=ifelse(harry_potter_support%v%'gender'==1,'blue','green'),
            edge.col="#CCCCCC55",
            output.mode = 'htmlWidget'
)
```

One challenge of constructing movies from matrices is that (as the authors of this dataset note) there is often a great deal of change between network survey panels.

*****
**Question:** How could dynamic network data (like in the example above) be collected differently to support animations and more flexible analysis of dynamics?

*****

## Importing event or spell data

The McFarland classroom interaction dataset is included as a `networkDynamic` object.  But the package also includes the raw tabular data used to construct the data, and we can use it as an example.  

First, we will read in the tab-delimited (`.tsv`) files for the edge and vertex data.

```{r}
# read vertex data
rawVerts<-read.table(paste(path.package('networkDynamic'),
   "/extdata/cls33_10_16_96_vertices.tsv",sep=''),header=TRUE,
   stringsAsFactors = FALSE)

# peek at column headings to find ids and times
head(rawVerts)
```

We can see that the first two columns of vertex data contain ids, the second and third column have the onset and terminus times (in minutes) and there are two vertex-level attributes: `sex` and `role`.

```{r}
# read in interaction (edge) data
rawEdges<-read.table(paste(path.package('networkDynamic'),
  "/extdata/cls33_10_16_96_edges.tsv",sep=''),header=TRUE,
  stringsAsFactors = FALSE)

# peek at column headings to find ids and times
head(rawEdges)
```

For the edges, we see the first two columns give the 'tail' and 'head' ids for the edges (referred to using the `vertex_id` we see in the vertex data), the onset and terminus times are in the third and forth columns, and there are attributes for `weight` and `interaction_type`.  Each row will  correspond to an edge-spell when data is loaded up, but the onset and terminus times are the same, so these will be momentary events. 

We will use the `networkDynamic()` function to construct the network. We will pass in the vertex data via the `vertex.spells` argument, but as it is expecting data in the order 'onset','terminus','id', we need to reorder the data.frame as we pass it in.  Similarly, the edge data must be ordered by 'onset','terminus','tail','head' to be processed correctly by the `edge.spells` argument.  

```{r}
cls33 <-networkDynamic(vertex.spells=rawVerts[,c(3,4,1)],
                       edge.spells=rawEdges[,c(3,4,1,2)])
```

This seems to have worked, but we didn't bring in the attribute data. For the edges, we can just include the extra columns and tell it what we want them named and it will create the appropriate dynamic attributes. 

```{r}
cls33 <-networkDynamic(vertex.spells=rawVerts[,c(3,4,1)],
                       edge.spells=rawEdges[,c(3,4,1,2,5,6)],  #<- add an extra column
                       create.TEAs = TRUE,
                       edge.TEA.names = c('weight','interaction_type'))  #<- include variable names
```

Check that it actually did it. 
```{r}
list.edge.attributes(cls33)
```

```{r}
cls33 <-networkDynamic(vertex.spells=rawVerts[,c(3,4,1,2)],
                       edge.spells=rawEdges[,c(3,4,1,2,5,6)],
                       create.TEAs = TRUE,
                       edge.TEA.names = c('weight','interaction_type'))
list.edge.attributes(cls33)
```

Since the `sex` and `role` of the vertices don't actually change, it will be better to assign them as simple static attributes in the network. 

```{r}
# add in the unchanging vertex attribute data
set.vertex.attribute(cls33,"sex",as.vector(rawVerts$sex))
set.vertex.attribute(cls33,"role",as.vector(rawVerts$role))
```

Now for some additional (and optional) book-keeping: we can also bring in the `data_id` -- which is the subject research id used across classrooms throughout the McFarland dataset -- and set it as the "persistent id". This allows us to easily translate from the vertex ids (which must always range from 1 to the size of the network) even when working with vertex subsets of the original network.  (See `?persistent.ids`)  

```{r}
set.vertex.attribute(cls33,"data_id",as.numeric(rawVerts$data_id))
set.network.attribute(cls33,'vertex.pid','data_id')
```

By default, `networkDynamic` created a `net.obs.period` object to describe the time range of the data.  Since we know from the variable names that the units are in minutes, we can update it as a helpful hint for our future selves. 

```{r}
cls33%n%'net.obs.period'
obs<-cls33%n%'net.obs.period'
obs$'time.unit'<-'minutes'
cls33%n%'net.obs.period'<-obs
```

Now that we've loaded in the data we can plot it to see if it appears as we might expect. We've already seen a number of animation examples using this data, so lets try a more sophisticated static plot.  We can write some functions to define how we would like to aggregate the edge attributes for plotting purposes. 

For example, since the data provides us with a `weight` attribute for each interaction, we can create a function to sum up all the weights in a given time period in order to compute a total weight for each edge.  The important detail here is that we specify `return.tea=TRUE` when fetching the dynamic edge attributes.  This means that it will give back the unaggregated list of matching elements for each edge instead of using the `rule` to return only the earliest or latest value. 

```{r}
eWeight<-function(net,onset,terminus){
   # get the appropriate edge attributes matching the interval
  vals<- get.edge.attribute.active(net,'weight',
                                   onset=onset,terminus=terminus,
                                   return.tea=TRUE) # return all matching tea values
  # now compute for each edge
  sapply(vals,function(eVal){
    # add up all the values for that edge
    sum(as.numeric(eVal[[1]]))
  })
}
```

The original research using this data used the interaction types to control the colors of the edges. We can create a function that -- when given the network and a time range -- will compute the percentages of each of the three interaction types recorded for each edge, and use that to generate a color value by mapping to the percentages of red, green, and blue.

```{r}
interactionColor<-function(net,onset,terminus){
  # get the appropriate edge attributes matching the interval
  vals<- get.edge.attribute.active(net,'interaction_type',
                                   onset=onset,terminus=terminus,
                                   return.tea=TRUE) # return all matching TEA values
  # aggregate for each edge
  eColors<-sapply(vals,function(eVal){
    # count up the number of values of each type
    redCount<-sum( eVal[[1]]=='sanction' )
    greenCount<-sum( eVal[[1]]=='task' )
    blueCount<-sum( eVal[[1]]=='social' )
    total<-redCount+greenCount+blueCount
    # compute percentages of interactions of each type
    # make it into a semi-transparent color using RGB specification
    color<-rgb(redCount/total,greenCount/total,blueCount/total,alpha = 0.5)
  })
  return(eColors)
}
  
```

Now we plot the aggregate network, mapping our new functions to the edge color and width and passing in the time ranges (if this was a movie, the ranges would be passed in automatically). 

```{r}
plot(cls33,
             edge.col=interactionColor(cls33,0,45),
             edge.lwd=eWeight(cls33,0,45),
             vertex.col='gray',
             vertex.cex=ifelse(cls33%v%'role'=='instructor',2,1), # make teachers bigger
             main='Classroom interactions aggregated over time\nblue=social, green=task, red=conflict'
             )
```

Interesting to see that one of the students is almost as central as the instructors. And that there appears to be one relationship that is almost entirely antagonistic...

## Importing other network formats (Pajek .net and SoNIA.son)

The `networkDynamic` package provides file import parsers for the SoNIA `.son`-formatted time event format.  See `?read.son' for examples. 

The `network` includes a `read.paj` function for parsing Pajek's `.net`- and `.paj` network data files. 

Lets peek at a trivial Pajek network file with timing provided on the Pajek site:
```{r}
cat(readLines('http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/Time.net'),sep='\n')
    
```
It is more or less a spell format, but with some wildcards.

When these network files include timing information, `read.paj` can be sneakily requested to output in a `networkDynamic` format by setting `time.format='networkDynamic'`

```{r}
pajekTime<-read.paj('http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/Time.net',
               time.format='networkDynamic')
pajekTime
```

We can print it out as spell data.  Notice that the single time elements in the input format were converted into a range -- 7 becomes 7-8
```{r}
# the edge time info
as.data.frame(pajekTime)
# the vertex time info
get.vertex.activity(pajekTime,as.spellList = TRUE)

```


# Advanced examples

## A more complete tergm/stergm example
This is an expanded version of the demo from the beginning of the tutorial. It illustrates how to run a `tergm` simulation and some additional useful features for working with `tergm` model output. 

Let say we want to construct a basic but plausible statistical model of a dynamic network defined as a STERGM, and we want to see what one possible realization of the network might look like.  Using statnet's `tergm` package, we can  estimate the parameters for an edge formation and dissolution process which produces a network similar to the Florentine business network (`?ergm::flobusiness`) given as input.  First we load up the data.

```{r,cache=FALSE}
require(tergm)    # lib for temporal ergm simulations
data("florentine") # an example network
plot(flobusiness,displaylabels=T)
```

Then we ask `stergm` to fit a model with a random edge probability ("edges") plus a type of clustering defined as a decreasing marginal return on the number of edge-wise shared partners ("gwesp"). We also include a random dissolution process on the edges to keep the density from simply increasing at each time step.  For more background on the modeling process please see the `tergm` workshop materials at http://statnet.org/workshops/SUNBELT/current/tergm/tergm_tutorial.html. 

```{r}
theta.diss <- log(9)
stergm.fit.1 <- stergm(flobusiness,
  formation= ~edges+gwesp(0,fixed=T), 
  dissolution = ~offset(edges),
  targets="formation",
  offset.coef.diss = theta.diss,  
  estimate = "EGMME"  )
```

After the model has been estimated, we can take a number of sequential draws from it to see how the network might "evolve" over time, and output these discrete  networks as a single `networkDynamic` object. 
```{r}
stergm.sim.example <- simulate.stergm(stergm.fit.1,
                    nsim=1, time.slices = 25)
```

Now that we have our dataset, it is time to render the movie. We will specify some render parameters using `render.par`.  The `show.stats` parameter accepts a tergm summary formula to be evaluated, and print the model statistics for each slice on the appropriate frame of the movie. We can specify the formula we used for formation: `~edges+gwesp(0,fixed=T)`

```{r}
render.par=list(show.time=TRUE,
                show.stats="~edges+gwesp(0,fixed=T)")
```

Although not as sophisticated as the diagnostics plots used in ergm, we can calculate the target statistics at each time point to see how they vary

```{r}
plot( tErgmStats(stergm.sim.example,'edges+gwesp(0,fixed=T)') )
```


Then we ask it to build the animation, passing in some of the standard `plot.network` graphics arguments to change the color of the edges and show the labels with a smaller size and blue color. As we are fairly familiar with the output by now, we can suppress it by adding a `verbose=FALSE` argument.
```{r,cache=FALSE}
render.d3movie(stergm.sim.example,render.par=render.par,
                 edge.col="darkgray",displaylabels=TRUE,
                 label.cex=.6,label.col="blue",verbose=FALSE,
                 output.mode = 'htmlWidget')
```

  
Notice that in addition to the labels on the bottom of the plot indicating which time step is being viewed, it also displays the network statistics of interest for the time step. When the `edges` parameter increases, you can see the density on the graph increase and the number of isolates decrease. Eventually the model corrects, and the parameter drifts back down. 

### Proximity timeline of an infection

The proximity timeline attempts to represent changes in the relative network distances between vertices over time.  It can reveal how clusters merge and split over time.  It also has the ability to use dynamic vertex attributes to control the colors of the splines linking the instances of the vertices.  Section 8 "Exploring proximity with timelines" of the ndtv package vignette has a good explanation and exploration of the features. 


## Transmission trees and constructed animations

For this example we will simulate a fictitious rumor transmission network using code from the "Making Lin Freeman's windsurfers gossip" section of the `networkDynamic` vignette, and then examine various ways to look at the transmission. Finally, we will construct a new movie and animated transition using the output of several networks and algorithms.

The code below defines a function to run the simulation, sets initial seeds (starts the rumor) and then runs the simulation. The EpiModel package (Jenness, et. al. 2014) includes much better utilities for simulating transmission networks with various realistic properties.  If you don't care about the details of the simulation, just execute the entire block of code below to load in the function. 

```{r}
# function to simulate transmission
runSim<-function(net,timeStep,transProb){
  # loop through time, updating states
  times<-seq(from=0,to=max(get.change.times(net)),by=timeStep)
  for(t in times){
    # find all the people who know and are active
    knowers <- which(!is.na(get.vertex.attribute.active(
      net,'knowsRumor',at=t,require.active=TRUE)))
    # get the edge ids of active friendships of people who knew
    for (knower in knowers){
      conversations<-get.edgeIDs.active(net,v=knower,at=t)
      for (conversation in conversations){
        # select conversation for transmission with appropriate prob
        if (runif(1)<=transProb){
          # update state of people at other end of conversations
          # but we don't know which way the edge points so..
          v<-c(net$mel[[conversation]]$inl,
                 net$mel[[conversation]]$outl)
          # ignore the v we already know and people who already know
          v<-v[!v%in%knowers]
          if (length(v)){
            activate.vertex.attribute(net,"knowsRumor",TRUE,
                                      v=v,onset=t,terminus=Inf)
            # record who spread the rumor
            activate.vertex.attribute(net,"heardRumorFrom",knower,
                                    v=v,onset=t,length=timeStep)
            # record which friendships the rumor spread across
            activate.edge.attribute(net,'passedRumor',
                      value=TRUE,e=conversation,onset=t,terminus=Inf)
          }
        }
      }
    }  
  }
  return(net)
}
```

We next need to load in the `networkDynamic` data object, set up the initial state of the simulation, and then use the function we defined above to propagate the rumor. 


```{r}
data(windsurfers)    # let's go to the beach!

# set initial params...
timeStep <- 1  # units are in days
transProb <- 0.2 # how likely to tell in each conversation/day
# start the rumor out on vertex 1
activate.vertex.attribute(windsurfers,"knowsRumor",TRUE,v=1,
                          onset=0-timeStep,terminus=Inf)
activate.vertex.attribute(windsurfers,"heardRumorFrom",1,v=1,
                          onset=0-timeStep,length=timeStep)
activate.edge.attribute(windsurfers,'passedRumor',value=FALSE,
onset=-Inf,terminus=Inf)
# run the sim!
windsurfers<-runSim(windsurfers,timeStep,transProb)
```

Now the windsurfers network should have dynamic attributes indicating who knows the rumor, who they heard it from, and which edges passed it. 

```{r}
list.vertex.attributes(windsurfers)
list.edge.attributes(windsurfers)
```

Lets plot the time-aggregate network with the infected vertices and edges highlighted by their status in the last time point
```{r}
# plot the aggregate network, hiliting infected
plot(windsurfers,
     vertex.col=ifelse(
       !is.na(get.vertex.attribute.active(windsurfers,'knowsRumor',at=31)),
       'red','#55555555'
     ),
     edge.col=ifelse(
       get.edge.attribute.active(windsurfers,'passedRumor',at=31),
       'red','#55555555'
     ),
     vertex.cex=0.8
)
```

From the plot, it appears the rumor stayed mostly in one of the communities. But without being able to see the timing of the infections, it is difficult to tell what is going on. Since we know that the high vertex turnover makes it hard to render this as a basic movie, we can create a "flip-book" style movie, where we will keep the vertex positions fixed and just animate the dynamics.

```{r}
# record the coords produced by plot
coords<-plot(windsurfers)
# set them as animation coords directly,without layout
activate.vertex.attribute(windsurfers, 'animation.x',coords[,1], 
                          onset=-Inf, terminus=Inf)
activate.vertex.attribute(windsurfers, 'animation.y',coords[,2],
                          onset=-Inf,terminus=Inf)

# construct slice par to indicate time range to render
windsurfers%n%'slice.par'<-list(start=-31,end=0,interval=1, 
                                aggregate.dur=31,rule='latest')
```

Now we will render it out to file, using functional plot arguments to color edges and vertices by their infection status at each time point. 

```{r,fig.keep='none',message=FALSE,results='hide'}
saveVideo(
  render.animation(windsurfers,
            render.par=list(initial.coords=coords),
            # color edges by rumor status       
            edge.col=function(slice){
              ifelse(slice%e%'passedRumor','red','#00000055')
            },
            # color vertices by rumor status       
            vertex.col=function(slice){
              ifelse(!is.na(slice%v%'knowsRumor'),'red','gray')
            },
            # change text of label to show time and total infected.        
            xlab=function(slice,terminus){
              paste('time:',terminus,' total infected:',
                    sum(slice%v%'knowsRumor',na.rm=TRUE))
            },       
            vertex.cex=0.8,label.cex=0.8,render.cache='none'
  )
  ,video.name='windsurferFlipbook.mp4'
)
```

Notice that we did something really funky with the `slice.par` parameters.  We are using `aggregate.dur=31`--equal to the entire duration of the network--and starting at -31. This makes it so we are effectively sliding along a giant bin which is gradually accumulating more of the network edges with each step until it contains the whole thing.  We also used an initial coordinate setting for the vertices (otherwise they would appear at zero when first entering) and functional attribute definitions for vertex and edge colors. 

*****
**Question:** Why does the infection fail to spread across many of the edges from infected vertices visible in this animation?

*****

In this view, it is still quite difficult to see the sequence of infections and the infection path.  We can try extracting the infection so that we can visualize it directly.  The function below will extract a network consisting only of the rumor-infected vertices and edges in the original network that passed the rumor.  The edges will be directed, so we can see it as a tree.  Don't need to look at this in detail, just load it up. 


```{r}
# function to extract the transmission tree
# as a directed network
transTree<-function(net){
  # for each vertex in net who knows
  knowers <- which(!is.na(get.vertex.attribute.active(net,
                                        'knowsRumor',at=Inf)))
  # find out who the first transmission was from
  transTimes<-get.vertex.attribute.active(net,"heardRumorFrom",
                      onset=-Inf,terminus=Inf,return.tea=TRUE)
  # subset to only ones that know
  transTimes<-transTimes[knowers]
  # get the first value of the TEA for each knower
  tellers<-sapply(transTimes,function(tea){tea[[1]][[1]]})
  # create a new net of appropriate size 
  treeIds <-union(knowers,tellers)
  tree<-network.initialize(length(treeIds),loops=TRUE)
  # copy labels from original net
  set.vertex.attribute(tree,'vertex.names',treeIds)
  # translate the knower and teller ids to new network ids   
  # and add edges for each transmission                
  add.edges(tree,tail=match(tellers,treeIds), 
            head=match(knowers,treeIds) )               
  return(tree)                
}
```

Now lets use the newly-created `transTree()` function to find the transmission tree, and plot it.

```{r, fig.width=7,fig.height=7}
windTree<-transTree(windsurfers)
plot(windTree,displaylabels=TRUE)
```

We don't necessarily have to use `compute.animation` to construct the sequence of coordinates we are going to render in a movie. We can assemble a new synthetic network to visualize and, if we are careful, we can even use coordinates from one layout and apply them to another.  In the next example, we will assemble an animated transition from the full cumulative network into a hierarchical representation of the transmission tree (this part requires a working installation of Graphviz).

First, lets compute a layout for the cumulative across-time network
```{r}
# calculate coord for aggregate network
windAni<-network.collapse(windsurfers,onset=-Inf,terminus=Inf,
                          rule='latest')
cumCoords<-plot.network(windAni)
cumCoords<-layout.normalize(cumCoords)
```

Next, compute a hierarchical tree layout of the transmission tree.
```{r}
# calculate coords for transmission tree
treeCoords<-network.layout.animate.Graphviz(windTree,
              layout.par=list(gv.engine='dot',
                              gv.args='-Granksep=4'))
treeCoords<-layout.normalize(treeCoords)
# peek at it
plot(windTree,coord=treeCoords,displaylabels=TRUE,
           jitter=FALSE,label.pos=1,label.cex=0.7,label.col='blue')
```

Now lets assemble a dynamic network on `windAni` frame-by-frame applying the coordinates we saved from the previous layouts of the cumulative and transmission tree networks.

For the first frame, we want all vertices and edges active and we attach the coordinates we calculated for the cumulative network to position the vertices. 
```{r}

activate.vertices(windAni,onset=0,terminus=1)
activate.edges(windAni,onset=0,terminus=1)
# store the plain network coords for cumulative network
activate.vertex.attribute(windAni,'animation.x',cumCoords[,1],
                          onset=0,terminus=Inf)
activate.vertex.attribute(windAni,'animation.y',cumCoords[,2],
                          onset=0,terminus=Inf)
```

For the second frame, we activate vertices that "know" and all the edges that passed the rumor.
```{r}
activate.vertices(windAni,onset=1,terminus=3,
                  v=which(windAni%v%'knowsRumor'))
activate.edges(windAni,onset=1,terminus=3,
               e=which(windAni%e%'passedRumor'))
```

For the third frame, the edges and vertices will still be active, but we want to transition the positions to the "tree", so we attach the tree coordinates at that time. 
```{r}

activate.vertex.attribute(windAni,'animation.x',treeCoords[,1],
          onset=2,terminus=Inf,v=network.vertex.names(windTree))
activate.vertex.attribute(windAni,'animation.y',treeCoords[,2],
          onset=2,terminus=Inf,v=network.vertex.names(windTree))
```

Once again we construct slice par to indicate time range to render
```{r}
windAni%n%'slice.par'<-list(start=0,end=2,interval=1, 
                            aggregate.dur=1,rule='latest')

```

And render it to a file
```{r,message=FALSE}
saveVideo(
  render.animation(windAni,
            edge.col=function(slice){
              ifelse(!is.na(slice%e%'passedRumor'),
                     'red','#00000055')
            },
            vertex.col=function(slice){
              ifelse(!is.na(slice%v%'knowsRumor'),
                     'red','gray')
            },
            vertex.cex=0.8,label.cex=0.8,label.pos=1,
                   render.cache='none'
  )
, video.name='windsurferTreeTransition.mp4')
```

*****
**Exercise:** Generate a similar movie, but use the coordinates of the non-hierarchical tree layout (i.e. don't use Graphviz)

*****

*****
**Exercise:** Choose one of the dynamic dataset (perhaps one from the `networkDynamicData` package) and construct an animation.

*****



# Installing ndtv's optional external dependencies

Assuming that you've already got `ndtv` installed, here are some more detailed instructions for installing some of the external system tools that can be used for saving out videos, higher quality layouts, and other layout engines. 

## Installing FFmpeg for saving animations
FFmpeg http://www.ffmpg.org  (or Libav https://libav.org/) are cross-platform tools for converting and rendering video content in various formats. It is used as an external library by the `animation` package to save out the animation as a movie file on disk. (see `?saveVideo` for more information.) The install instructions are somewhat different on each platform.  You can access these instructions using `?install.ffmpeg`
```{r}
?install.ffmpeg   # help page for installing ffmpeg
```



## Installing Java and MDSJ setup
To use the MDSJ (Algorithmics Group, University of Konstanz 2009) layout algorithm, you must have Java installed on your system. If it is not installed, you can download it from http://www.java.com/en/download/index.jsp. On Windows, you may need to edit your "Path" environment variable to make Java executable from the command-line. Oracle provides some instructions for editing the Path: http://www.java.com/en/download/help/path.xml

When java is installed correctly the following command should print out the version information:
```{r}
system('java -version')
```

Due to CRAN's license restrictions, necessary components of the MDSJ layout (which we will use in a minute) are not distributed with `ndtv`.  Instead, the first time the MDSJ layout is called after installing or updating the `ndtv` package, it is going to ask to download the library.  Lets do that now on a pretend movie to get it out of the way:

```{r,message=FALSE,results='hide'}
network.layout.animate.MDSJ(network.initialize(1))
```


This will give a prompt like

```
The MDSJ Java library does not appear to be installed. 
The ndtv package can use MDSJ to provide a fast 
accurate layout algorithm. It can be downloaded from 
http://www.inf.uni-konstanz.de/algo/software/mdsj/
Do you want to download and install the MDSJ Java library? (y/N):
```

Responding `y` to the prompt should install the library and print the following message:
```{r,echo=FALSE}
# the command above will default to not installing MDSJ in a non-interactive session
# so to make sure it is installed for this sweave build, call it internally
mdsj.dir <- file.path(path.package("ndtv"), "java/")
ndtv:::install.mdsj(mdsj.dir)
```

And its good to go! (unless you were intending to use the layout for commercial work...)

## Installing Graphviz
Graphviz is *not* required for `ndtv` to work.  However it does provide several interesting layouts including the hierarchical tree layout we used in one of the advanced examples. Platform specific instructions for installing Graphviz can be shown with `?install.graphviz`.





# Miscelaneous topics
## Compressing video output
\label{sec:compressing}
Saving the video output from an animation often produces very large files. These may cause problems for your viewers if you upload them directly to the web.  It is almost always a good idea to compress the video, as a dramatically smaller file can usually be created with little or no loss of quality. Although it may be possible to give `saveVideo()` various `other.opts` to control video compression, determining the right settings can be a trial and error process. The default settings for ffmpeg differ quite a bit depending on platform, some installations may give decent compression without tweaking the settings.  As an alternative, Handbrake http://handbrake.fr/ is an excellent and easy to use graphical tool for doing video compression into the web-standard H.264 codec with appropriate presets.

## Transparent colors
Using a bit of transparency can help a lot with readability for many visualizations. Transparency makes it so that overlapping edges can show through each other and the less saturated colors tend to be less distracting. Many of the R plot devices support transparency, but specifying the color codes with transparency can be a bit awkward. One way we demonstrated is to include an alpha  parameter to the `rgb()` function which defines a color given numeric values for proportions of red, green, blue, and alpha. In this context "alpha" is the computer graphics term for transparency.  
```{r}
# 50% blue
rgb(0,0,1,0.5)
```

If you want to just make one of R's existing named colors more transparent,  try `grDevices::adjustcolor()`. 
```{r}
# 50% pink
grDevices::adjustcolor('pink',alpha.f=0.5)
```

Notice that the output of each of these functions is a cryptic-looking string. These are HTML color codes, which are the most concise way to specify colors. These are 8-"digit" hexadecimal strings in the format`"#RRGGBBAA"`. Each hexadecimal "digit" has 16 possible values, ranging from 0 to F. The first pair of digits (RR) gives the percent of red, the second (BB) blue, third (GG) green, and last (AA) gives the alpha  percent. For example, 50% black is `"#00000088"`, 50% green would be `"#00FF0088"`.  These can be hard to remember, but useful once you have written down the colors you want.  

```{r}
# plot example net with 10% green
# 50% blue and 50% pink
colorNet<-network.initialize(5,directed=FALSE)
colorNet[,]<-1
plot(colorNet,edge.lwd=20,
     edge.col=c(rgb(0,1,0,0.1),"#0000FF80","#FFC0CB80"))
```

## Setting background colors and margins
You may have noticed that the network plots we have seen so far have fairly wide margins which allow extra room for labels and annotations.  It is possible to adjust the margins, and other generic plot commands, by passing in `par` arguments to `render.animation` via `plot.par`.  For example, we can set all of the margins to zero with the `mar` command and change the background to gray with `bg='gray'`.  See `?par` for a list of high-level plot parameters suitable for `plot.par`.
```{r,fig.keep='none',message=FALSE}
render.animation(wheel,plot.par=list(bg='gray',mar=c(0,0,0,0)),
                 edge.col='white')
```

## Tips for working with large networks
As the `msm.sim` example probably demonstrated, rendering animations of large networks can be very computationally intensive.  Here are a number of techniques we have found effective for working with networks that take a lot of time or are simply too large to render directly as animations.

* Test and refine algorithm settings and graphics parameters on a short sequence or single time slice of larger network before running the animation for its  full duration 
* Render full animations of large networks directly to disk instead previewing in the R plot window.  See the use of the `saveVideo` and `render.cache='none'` arguments in example in the Output Formats section. 
* Extract and visualize a relevant subset of the network.  For example, for a movie illustrating the effects of concurrency we were able to effectively visualize the relationships among the ~800-vertex infected component extracted from a simulation with a population of 10,000: http://statnet.org/movies/. Of course, displaying only a sub-network probably introduces some bias into the viewer's perception of the network's overall properties. 


# How to get help
Here are some suggestions on where to look for help if you run into problems or have questions:

* R's built in documentation feature. Each function has a help page, usually with some examples: i.e. `?render.animation`.  The listing of all the documentation pages can be found with `help(package='ndtv')` or `help(package='networkDynamic')`
* The included package vignettes: `browseVignettes(package='ndtv')`
* The statnet wiki has various FAQ pages and resources: https://statnet.org/trac/wiki
* You can always subscribe to the statnet mailing list and post your problem there: https://mailman2.u.washington.edu/mailman/listinfo/statnet_help


# Limitations
Before we create unreasonable expectations, we should be clear that you can't just throw any network into `render.animation` and expect good results.

* This is not a "big data" tool. So far we've mostly used `ndtv` successfully with networks of <1k vertices and several hundred time steps, but that takes a long time to render. 
* Animations of dense or fully-connected networks may not be useful. 
* The animation techniques work best when a relatively small number of ties are changing between time slices and vertex turnover rates (births and death) are low. 
* You may need to think carefully about how to aggregate and smooth the dynamics over time in order to reveal the underlying patterns of interest.  This is analogous to choosing bin-widths for histograms in order to reveal the distributional form of the data.
* Good results may require considering how the weights and measures of your input data can be translated meaningfully to the implicit "space" you are embedding your data in.

As these packages are still very much under development, we would greatly appreciate your suggestions and feedback: `skyebend@skyeome.net`

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Michalec, G.. Bender-deMoll, S.,  Morris, M. (2014) 'ndtv-d3: an HTML5 network animation player for the ndtv package' The statnet project.   https://github.com/statnet/ndtv-d3


Xie Y (2012).
"animation: An R Package for Creating Animations and Demonstrating Statistical Methods."
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# Package versions

This tutorial was compiled from Rmarkdown using the following package versions:

```{r}
date()
sessionInfo()
```

