<?xml version="1.0"?>
<!DOCTYPE chapter PUBLIC "-//OASIS//DTD DocBook XML V4.3//EN"
               "http://www.oasis-open.org/docbook/xml/4.3/docbookx.dtd" [
<!ENTITY igraph "igraph">
]>

<chapter id="igraph-Structural">
<title>Structural properties of graphs</title>

<!-- doxrox-include about_structural -->

<section id="basic-properties"><title>Basic properties</title>
<!-- doxrox-include igraph_are_adjacent -->
</section>

<section id="Sparsifiers"><title>Sparsifiers</title>
<!-- doxrox-include igraph_spanner -->
</section>

<section id="shortest-path-related-functions"><title>(Shortest)-path related functions</title>
<!-- doxrox-include igraph_distances -->
<!-- doxrox-include igraph_distances_cutoff -->
<!-- doxrox-include igraph_distances_dijkstra -->
<!-- doxrox-include igraph_distances_dijkstra_cutoff -->
<!-- doxrox-include igraph_distances_bellman_ford -->
<!-- doxrox-include igraph_distances_johnson -->
<!-- doxrox-include igraph_distances_floyd_warshall -->
<!-- doxrox-include igraph_get_shortest_paths -->
<!-- doxrox-include igraph_get_shortest_path -->
<!-- doxrox-include igraph_get_shortest_paths_dijkstra -->
<!-- doxrox-include igraph_get_shortest_path_dijkstra -->
<!-- doxrox-include igraph_get_shortest_paths_bellman_ford -->
<!-- doxrox-include igraph_get_shortest_path_bellman_ford -->
<!-- doxrox-include igraph_get_shortest_path_astar -->
<!-- doxrox-include igraph_astar_heuristic_func_t -->
<!-- doxrox-include igraph_get_all_shortest_paths -->
<!-- doxrox-include igraph_get_all_shortest_paths_dijkstra -->
<!-- doxrox-include igraph_get_k_shortest_paths -->
<!-- doxrox-include igraph_get_all_simple_paths -->
<!-- doxrox-include igraph_average_path_length -->
<!-- doxrox-include igraph_average_path_length_dijkstra -->
<!-- doxrox-include igraph_path_length_hist -->
<!-- doxrox-include igraph_diameter -->
<!-- doxrox-include igraph_diameter_dijkstra -->
<!-- doxrox-include igraph_girth -->
<!-- doxrox-include igraph_eccentricity -->
<!-- doxrox-include igraph_eccentricity_dijkstra -->
<!-- doxrox-include igraph_radius -->
<!-- doxrox-include igraph_radius_dijkstra -->
<!-- doxrox-include igraph_graph_center -->
<!-- doxrox-include igraph_graph_center_dijkstra -->
<!-- doxrox-include igraph_pseudo_diameter -->
<!-- doxrox-include igraph_pseudo_diameter_dijkstra -->
<!-- doxrox-include igraph_voronoi -->
<!-- doxrox-include igraph_vertex_path_from_edge_path -->
</section>

<section id="widest-path-related-functions"><title>Widest-path related functions</title>
<!-- doxrox-include igraph_get_widest_path -->
<!-- doxrox-include igraph_get_widest_paths -->
<!-- doxrox-include igraph_widest_path_widths_dijkstra -->
<!-- doxrox-include igraph_widest_path_widths_floyd_warshall -->
</section>

<section id="efficiency-measures"><title>Efficiency measures</title>
<!-- doxrox-include igraph_global_efficiency -->
<!-- doxrox-include igraph_local_efficiency -->
<!-- doxrox-include igraph_average_local_efficiency -->
</section>

<section id="neighborhood-of-a-vertex"><title>Neighborhood of a vertex</title>
<!-- doxrox-include igraph_neighborhood_size -->
<!-- doxrox-include igraph_neighborhood -->
<!-- doxrox-include igraph_neighborhood_graphs -->
</section>

<section id="local-scan-statistics"><title>Local scan statistics</title>
<!-- doxrox-include about_local_scan -->
<section id="us-statistics"><title>"Us" statistics</title>
<!-- doxrox-include igraph_local_scan_0 -->
<!-- doxrox-include igraph_local_scan_1_ecount -->
<!-- doxrox-include igraph_local_scan_k_ecount -->
</section>
<section id="them-statistics"><title>"Them" statistics</title>
<!-- doxrox-include igraph_local_scan_0_them -->
<!-- doxrox-include igraph_local_scan_1_ecount_them -->
<!-- doxrox-include igraph_local_scan_k_ecount_them -->
</section>
<section id="pre-calculated-subsets"><title>Pre-calculated subsets</title>
<!-- doxrox-include igraph_local_scan_neighborhood_ecount -->
<!-- doxrox-include igraph_local_scan_subset_ecount -->
</section>
</section>

<section id="graph-components"><title>Graph components</title>
<!-- doxrox-include igraph_subcomponent -->
<!-- doxrox-include igraph_connected_components -->
<!-- doxrox-include igraph_clusters -->
<!-- doxrox-include igraph_is_connected -->
<!-- doxrox-include igraph_decompose -->
<!-- doxrox-include igraph_decompose_destroy -->
<!-- doxrox-include igraph_reachability -->
<!-- doxrox-include igraph_count_reachable -->
<!-- doxrox-include igraph_transitive_closure -->
<!-- doxrox-include igraph_biconnected_components -->
<!-- doxrox-include igraph_articulation_points -->
<!-- doxrox-include igraph_bridges -->
<!-- doxrox-include igraph_is_biconnected -->
</section>

<section id="degree-sequences"><title>Degree sequences</title>
<!-- doxrox-include igraph_is_graphical -->
<!-- doxrox-include igraph_is_bigraphical -->
</section>

<section id="centrality-measures"><title>Centrality measures</title>
<!-- doxrox-include igraph_closeness -->
<!-- doxrox-include igraph_harmonic_centrality -->
<!-- doxrox-include igraph_betweenness -->
<!-- doxrox-include igraph_edge_betweenness -->
<!-- doxrox-include igraph_pagerank_algo_t -->
<!-- doxrox-include igraph_pagerank -->
<!-- doxrox-include igraph_personalized_pagerank -->
<!-- doxrox-include igraph_personalized_pagerank_vs -->
<!-- doxrox-include igraph_constraint -->
<!-- doxrox-include igraph_maxdegree -->
<!-- doxrox-include igraph_strength -->
<!-- doxrox-include igraph_eigenvector_centrality -->
<!-- doxrox-include igraph_hub_and_authority_scores -->
<!-- doxrox-include igraph_convergence_degree -->
</section>

<section id="range-limited-centrality-measures"><title>Range-limited centrality measures</title>
<!-- doxrox-include igraph_closeness_cutoff -->
<!-- doxrox-include igraph_harmonic_centrality_cutoff -->
<!-- doxrox-include igraph_betweenness_cutoff -->
<!-- doxrox-include igraph_edge_betweenness_cutoff -->
</section>

<section id="subset-limited-centrality-measures"><title>Subset-limited centrality measures</title>
<!-- doxrox-include igraph_betweenness_subset -->
<!-- doxrox-include igraph_edge_betweenness_subset -->
</section>

<section id="centralization"><title>Centralization</title>
<!-- doxrox-include igraph_centralization -->
<!-- doxrox-include igraph_centralization_degree -->
<!-- doxrox-include igraph_centralization_betweenness -->
<!-- doxrox-include igraph_centralization_closeness -->
<!-- doxrox-include igraph_centralization_eigenvector_centrality -->
<!-- doxrox-include igraph_centralization_degree_tmax -->
<!-- doxrox-include igraph_centralization_betweenness_tmax -->
<!-- doxrox-include igraph_centralization_closeness_tmax -->
<!-- doxrox-include igraph_centralization_eigenvector_centrality_tmax -->
</section>

<section id="similarity-measures"><title>Similarity measures</title>
<!-- doxrox-include igraph_bibcoupling -->
<!-- doxrox-include igraph_cocitation -->
<!-- doxrox-include igraph_similarity_jaccard -->
<!-- doxrox-include igraph_similarity_jaccard_pairs -->
<!-- doxrox-include igraph_similarity_jaccard_es -->
<!-- doxrox-include igraph_similarity_dice -->
<!-- doxrox-include igraph_similarity_dice_pairs -->
<!-- doxrox-include igraph_similarity_dice_es -->
<!-- doxrox-include igraph_similarity_inverse_log_weighted -->
</section>

<section id="trees"><title>Trees and forests</title>
<!-- doxrox-include igraph_minimum_spanning_tree -->
<!-- doxrox-include igraph_minimum_spanning_tree_unweighted -->
<!-- doxrox-include igraph_minimum_spanning_tree_prim -->
<!-- doxrox-include igraph_random_spanning_tree -->
<!-- doxrox-include igraph_is_tree -->
<!-- doxrox-include igraph_is_forest -->
<!-- doxrox-include igraph_to_prufer -->
</section>

<section id="transitivity-or-clustering-coefficient"><title>Transitivity or clustering coefficient</title>
<!-- doxrox-include igraph_transitivity_undirected -->
<!-- doxrox-include igraph_transitivity_local_undirected -->
<!-- doxrox-include igraph_transitivity_avglocal_undirected -->
<!-- doxrox-include igraph_transitivity_barrat -->
<!-- doxrox-include igraph_ecc -->
</section>

<section id="directedness-conversion"><title>Directedness conversion</title>
<!-- doxrox-include igraph_to_directed -->
<!-- doxrox-include igraph_to_undirected -->
</section>

<section id="spectral-properties"><title>Spectral properties</title>
<!-- doxrox-include igraph_get_laplacian -->
<!-- doxrox-include igraph_get_laplacian_sparse -->
<!-- doxrox-include igraph_laplacian_normalization_t -->
</section>

<section id="non-simple-graphs-multiple-and-loop-edges"><title>Non-simple graphs: Multiple and loop edges</title>
<!-- doxrox-include igraph_is_simple -->
<!-- doxrox-include igraph_is_loop -->
<!-- doxrox-include igraph_has_loop -->
<!-- doxrox-include igraph_count_loops -->
<!-- doxrox-include igraph_is_multiple -->
<!-- doxrox-include igraph_has_multiple -->
<!-- doxrox-include igraph_count_multiple -->
<!-- doxrox-include igraph_count_multiple_1 -->
</section>

<section id="mixing-patterns"><title>Mixing patterns</title>
<!-- doxrox-include igraph_assortativity_nominal -->
<!-- doxrox-include igraph_assortativity -->
<!-- doxrox-include igraph_assortativity_degree -->
<!-- doxrox-include igraph_joint_type_distribution -->
<!-- doxrox-include igraph_joint_degree_distribution -->
<!-- doxrox-include igraph_joint_degree_matrix -->
</section>

<section id="k-cores"><title>K-cores and k-trusses</title>
<!-- doxrox-include igraph_coreness -->
<!-- doxrox-include igraph_trussness -->
</section>

<section id="topological-sorting-directed-acyclic-graphs"><title>Topological sorting, directed acyclic graphs</title>
<!-- doxrox-include igraph_is_dag -->
<!-- doxrox-include igraph_topological_sorting -->
<!-- doxrox-include igraph_feedback_arc_set -->
<!-- doxrox-include igraph_feedback_vertex_set -->
</section>

<section id="maximum-cardinality-search-chordal-graphs"><title>Maximum cardinality search and chordal graphs</title>
<!-- doxrox-include igraph_maximum_cardinality_search -->
<!-- doxrox-include igraph_is_chordal -->
</section>

<section id="matchings"><title>Matchings</title>
<!-- doxrox-include igraph_is_matching -->
<!-- doxrox-include igraph_is_maximal_matching -->
<!-- doxrox-include igraph_maximum_bipartite_matching -->
</section>

<section id="unfolding-a-graph-into-a-tree"><title>Unfolding a graph into a tree</title>
<!-- doxrox-include igraph_unfold_tree -->
</section>

<section id="other-operations"><title>Other operations</title>
<!-- doxrox-include igraph_density -->
<!-- doxrox-include igraph_mean_degree -->
<!-- doxrox-include igraph_reciprocity -->
<!-- doxrox-include igraph_diversity -->
<!-- doxrox-include igraph_is_mutual -->
<!-- doxrox-include igraph_has_mutual -->
<!-- doxrox-include igraph_avg_nearest_neighbor_degree -->
<!-- doxrox-include igraph_degree_correlation_vector -->
<!-- doxrox-include igraph_get_adjacency -->
<!-- doxrox-include igraph_get_adjacency_sparse -->
<!-- doxrox-include igraph_get_stochastic -->
<!-- doxrox-include igraph_get_stochastic_sparse -->
<!-- doxrox-include igraph_get_edgelist -->
<!-- doxrox-include igraph_is_acyclic -->
</section>

<section id="structural-properties-deprecated"><title>Deprecated functions</title>
<!-- doxrox-include igraph_are_connected -->
<!-- doxrox-include igraph_shortest_paths -->
<!-- doxrox-include igraph_shortest_paths_dijkstra -->
<!-- doxrox-include igraph_shortest_paths_bellman_ford -->
<!-- doxrox-include igraph_shortest_paths_johnson -->
<!-- doxrox-include igraph_get_stochastic_sparsemat -->
<!-- doxrox-include igraph_get_sparsemat -->
<!-- doxrox-include igraph_laplacian -->
<!-- doxrox-include igraph_hub_score -->
<!-- doxrox-include igraph_authority_score -->
</section>

</chapter>
