Module properties 

Graph properties — invariants and metrics. Phase 1 entries: ALGO-PR-001 (girth), ALGO-PR-002 (triangles + global/local transitivity), ALGO-PR-003 (density + mean distance), ALGO-PR-004 (reciprocity), ALGO-PR-005 (avg nearest-neighbour degree), ALGO-PR-006 (degree assortativity).

Structs

BipartiteResult

Result of bipartiteness check.

CentralizationResult

Result of a centralization convenience wrapper.

ClosenessCutoffResult

Result of closeness_cutoff.

EigenvectorScores

Output of eigenvector_centrality_full: the normalised centrality vector and the dominant eigenvalue of the (possibly shifted-back) adjacency matrix.

GetBiadjacencyResult

Result of get_biadjacency_matrix.

GetBiadjacencyWeightedResult

Result of get_biadjacency_weighted.

HitsScores

Output of hub_and_authority_scores: scaled hub and authority vectors and the dominant eigenvalue of A·Aᵀ.

PowerLawFitResult

Result of fitting a power-law distribution to a sample.

StronglyRegularParams

Result of strongly regular graph recognition.

UnfoldTreeResult

Result of unfolding a graph into a tree.

Enums

AdjacencyType

Which triangle of the adjacency matrix to fill (undirected graphs only).

CentralizationMode

Whether centralization considers in-degree, out-degree, or total.

CorenessMode

Direction-handling for coreness_with_mode.

DegreeMode

Direction mode for degree computation in directed graphs.

EdgeTypeFilter

What kinds of edges are allowed when testing graphicality.

EigenvectorMode

How to consider edge directions for eigenvector_centrality_full and friends. Mirrors upstream’s IGRAPH_OUT / IGRAPH_IN / IGRAPH_ALL.

LaplacianNormalization

Laplacian normalization mode.

LoopHandling

How to count self-loop edges in the adjacency matrix diagonal.

LoopMode

How loops are counted when computing degree centralization.

NeighborhoodMode

Direction mode for neighborhood_size_with_mode on directed graphs. Ignored on undirected graphs — every mode reduces to NeighborhoodMode::All.

ReciprocityMode

Reciprocity formula choice. Counterpart of upstream’s igraph_reciprocity_t (IGRAPH_RECIPROCITY_DEFAULT / IGRAPH_RECIPROCITY_RATIO).

SimpleMode

Direction-handling for is_simple_with_mode. Counterpart of upstream’s directed boolean parameter.

SortOrder

Sort order for vertex degree sorting.

StrengthMode

Direction mode for strength_with_mode on directed graphs. Ignored on undirected graphs.

TransitivityMode

How to handle vertices with degree < 2 when averaging local transitivity.

Functions

are_adjacent

Check whether two vertices are connected by at least one edge.

assortativity

Value-based assortativity coefficient of graph.

assortativity_degree

Degree assortativity coefficient of graph (undirected, unweighted). Returns None for graphs with no edges or for regular graphs (all vertices same degree — the variance denominator vanishes, matching upstream’s IGRAPH_NAN).

assortativity_degree_directed

Directed degree assortativity coefficient (ALGO-PR-006c).

assortativity_degree_directed_weighted

Directed weighted degree assortativity (PR-006d).

assortativity_degree_weighted

Weighted degree assortativity coefficient.

assortativity_nominal

Compute categorical (nominal) assortativity coefficient.

average_local_efficiency

Average of local_efficiency over all N vertices. By upstream convention, returns 0.0 when vcount < 3 (no vertex can have two distinct neighbours, so every per-vertex value is trivially 0).

avg_nearest_neighbor_degree

Average nearest-neighbour degree, per vertex.

betweenness

Per-vertex (unweighted) betweenness centrality.

betweenness_cutoff

Range-limited betweenness centrality.

betweenness_subset

Subset betweenness centrality.

betweenness_weighted

Per-vertex weighted betweenness centrality.

bibcoupling

Computes bibliographic coupling scores between all pairs of vertices.

centralization

Compute the graph-level centralization score from per-vertex scores.

centralization_betweenness_tmax

Theoretical maximum betweenness centralization for a star graph.

centralization_betweenness_wrapper

Betweenness centralization: compute per-vertex betweenness scores and the graph-level centralization in one call.

centralization_closeness_tmax

Theoretical maximum closeness centralization for a star graph.

centralization_closeness_wrapper

Closeness centralization: compute per-vertex closeness scores and the graph-level centralization in one call.

centralization_degree_tmax

Theoretical maximum degree centralization for a star graph.

centralization_degree_wrapper

Degree centralization: compute per-vertex degree scores and the graph-level centralization in one call.

centralization_eigenvector_tmax

Theoretical maximum eigenvector centralization for a star graph.

centralization_eigenvector_wrapper

Eigenvector centralization: compute per-vertex eigenvector centrality scores and the graph-level centralization in one call.

closeness

Per-vertex closeness centrality (Vec<Option<f64>>).

closeness_cutoff

Range-limited closeness centrality.

closeness_weighted

Per-vertex weighted closeness centrality.

cocitation

Computes the cocitation scores between all pairs of vertices.

constraint

Compute Burt’s constraint scores for all vertices.

convergence_degree

Per-edge convergence degree.

convergence_degree_full

Convergence degree along with the per-edge In(e) / Out(e) counts.

coreness

Per-vertex coreness number.

coreness_with_mode

Coreness with explicit CorenessMode (ALGO-PR-015b).

count_adjacent_triangles

Per-vertex adjacent-triangle count. Entry i is the number of triangles vertex i participates in. Parallel edges and self-loops are ignored — the simple graph induced by the OUT-neighbour view is used (consistent with count_triangles). For directed graphs that is not yet the underlying-undirected projection that upstream uses; see ALGO-PR-002 for the deferred fix.

count_loops

Counts self-loop edges in graph.

count_multiple

Per-edge multiplicity: how many edges share each edge’s endpoint pair.

count_multiple_1

Multiplicity of a single edge: how many edges share the same endpoint pair as edge eid.

count_mutual

Count the number of mutual edge pairs in a directed graph.

count_triangles

Count the number of triangles in graph. Edge directions, parallel edges, and self-loops are ignored.

degeneracy

Return the degeneracy of a graph.

degree_correlation_vector

Compute the degree correlation function k_nn(k).

degree_distribution

Compute the degree distribution histogram of a graph.

degree_sequence

Returns the degree sequence of the graph.

density

Edge density of graph. Counterpart of igraph_density(_, NULL_weights, _, /*loops=*/false).

diversity

Structural diversity index for all vertices in an undirected graph.

ecc

Compute the edge clustering coefficient for eids in graph.

edge_betweenness

Per-edge unweighted betweenness centrality.

edge_betweenness_cutoff

Range-limited edge betweenness centrality.

edge_betweenness_subset

Subset edge betweenness centrality.

edge_betweenness_weighted

Per-edge weighted betweenness centrality (Vec<f64>).

eigenvector_centrality

Backward-compatible undirected, unweighted entry point.

eigenvector_centrality_directed

Directed unweighted eigenvector centrality.

eigenvector_centrality_directed_weighted

Directed weighted eigenvector centrality.

eigenvector_centrality_full

Master entry point matching upstream’s signature.

eigenvector_centrality_weighted

Undirected weighted eigenvector centrality.

expand_path_to_pairs

Expand a vertex path into consecutive pairs for edge lookup.

get_adjacency

Compute the adjacency matrix of a graph.

get_biadjacency_matrix

Extract the biadjacency matrix from a bipartite graph.

get_biadjacency_weighted

Extract a weighted biadjacency matrix from a bipartite graph.

get_edgelist

Return all edges of the graph as a list of (source, target) pairs.

get_eids

Look up edge IDs for a batch of vertex pairs.

get_laplacian

Compute the Laplacian matrix of a graph.

get_stochastic

Compute the stochastic adjacency matrix of a graph.

girth

Shortest cycle length in graph. Returns None for acyclic graphs.

global_efficiency

Global efficiency of graph — average inverse pairwise shortest distance over all N*(N-1) ordered vertex pairs. Pairs that are unreachable contribute 0.

harmonic_centrality

Per-vertex harmonic centrality.

harmonic_centrality_cutoff

Range-limited harmonic centrality.

harmonic_centrality_weighted

Per-vertex weighted harmonic centrality.

has_loop

Returns true iff graph has at least one self-loop edge.

has_multiple

Returns true iff graph has at least one parallel edge.

has_mutual

Check whether a directed graph has any mutual (reciprocal) edges.

hub_and_authority_scores

Compute Kleinberg’s hub and authority scores.

is_acyclic

Returns true iff graph contains no cycle.

is_apex_forest

Check whether a graph is an apex forest.

is_apex_tree

Check whether a graph is an apex tree.

is_banner_free

Check whether a graph is banner-free (no induced banner / flag).

is_biclique

Check whether a graph is a complete bipartite graph (biclique).

is_bigraphical

Test whether a bi-degree-sequence is bigraphical (realizable as a bipartite graph).

is_bipartite

Check whether a graph is bipartite and optionally return the partition.

is_biregular

Check whether a graph is biregular.

is_block_graph

Check whether a graph is a block graph.

is_bowtie_free

Check whether a graph is bowtie-free (no induced bowtie / butterfly).

is_bull_free

Check whether a graph is bull-free.

is_c4_free

Check whether a graph is C_4-free (no induced 4-cycle).

is_c5_free

Check whether a graph is C_5-free (no induced 5-cycle).

is_cactus_graph

Check whether a graph is a cactus graph.

is_caterpillar

Check whether a graph is a caterpillar tree.

is_chain_graph

Check whether a graph is a chain graph.

is_chordal_bipartite

Check whether a graph is chordal bipartite.

is_claw_free

Check whether a graph is claw-free.

is_clique

Check whether a set of vertices forms a clique.

is_cluster_graph

Check whether a graph is a cluster graph (disjoint union of cliques).

is_co_bipartite

Check whether a graph is co-bipartite.

is_co_chordal

Check whether a graph is co-chordal (complement is chordal).

is_cograph

Check whether a graph is a cograph (P4-free).

is_complete

Returns true iff every pair of distinct vertices is adjacent.

is_complete_bipartite

Check whether a graph is complete bipartite.

is_complete_multipartite

Check whether a graph is a complete multipartite graph.

is_cricket_free

Check whether a graph is cricket-free.

is_cubic

Check whether a graph is cubic (3-regular).

is_cycle

Check whether a graph is a cycle graph.

is_dag

Returns true iff graph is a directed acyclic graph.

is_dart_free

Check whether a graph is dart-free (no induced dart).

is_diamond_free

Check whether a graph is diamond-free.

is_distance_hereditary

Check whether a graph is distance-hereditary.

is_forest

Returns Some(roots) iff graph is a forest under mode, otherwise None. The null graph is a forest with empty roots.

is_fork_free

Check whether a graph is fork-free (no induced fork / cross).

is_gem_free

Check whether a graph is gem-free.

is_geodetic

Check whether a graph is geodetic.

is_graphical

Test whether a degree sequence is graphical (realizable as some graph).

is_house_free

Check whether a graph is house-free (no induced house graph).

is_independent_vertex_set

Check whether a set of vertices forms an independent set.

is_k_degenerate

Check whether a graph is k-degenerate.

is_lobster

Check whether a graph is a lobster tree.

is_loop

Returns a per-edge boolean vector marking self-loops.

is_multiple

Returns a per-edge boolean vector marking multiple (parallel) edges.

is_mutual

Check whether each edge in a directed graph is mutual (reciprocated).

is_net_free

Check whether a graph is net-free (no induced net subgraph).

is_outerplanar

Check whether a graph is outerplanar.

is_p5_free

Check whether a graph is P_5-free (no induced path on 5 vertices).

is_path

Check whether a graph is a path graph.

is_paw_free

Check whether a graph is paw-free.

is_perfect

Returns true when graph is a perfect graph.

is_proper_interval

Check whether a graph is a proper interval graph.

is_pseudo_forest

Check whether a graph is a pseudo-forest.

is_ptolemaic

Check whether a graph is ptolemaic.

is_regular

Check whether a graph is regular.

is_self_complementary

Check whether a graph is self-complementary.

is_semicomplete

Check whether a directed graph is semicomplete.

is_series_parallel

Check whether a graph is series-parallel.

is_simple

Returns true if graph has neither self-loops nor parallel edges.

is_simple_with_mode

is_simple with explicit SimpleMode (ALGO-PR-013b).

is_spider

Check whether a graph is a spider graph.

is_split_graph

Check whether a graph is a split graph.

is_star

Check whether a graph is a star graph.

is_strongly_chordal

Check whether a graph is strongly chordal.

is_strongly_regular

Check whether a graph is strongly regular.

is_threshold_graph

Check whether a graph is a threshold graph.

is_tournament

Check whether a graph is a tournament.

is_tree

Returns Some(root) iff graph is a tree under mode, otherwise None. The null graph (vcount == 0) is not a tree by convention.

is_triangle_free

Test whether a graph is triangle-free.

is_trivially_perfect

Check whether a graph is trivially perfect.

is_unicyclic

Check whether a graph is unicyclic.

is_weakly_chordal

Check whether a graph is weakly chordal.

is_well_covered

Check whether a graph is well-covered.

is_wheel

Check whether a graph is a wheel graph.

is_windmill

Check whether a graph is a windmill graph.

joint_degree_distribution

Compute the joint degree distribution matrix.

joint_degree_matrix

Compute the joint degree matrix of a graph.

joint_type_distribution

Compute the joint type distribution (mixing matrix).

list_triangles

List all triangles in a graph.

local_efficiency

Per-vertex local efficiency. For each vertex v, computes the average inverse distance between every ordered pair of distinct vertices in N(v) (the unique non-self neighbours of v), measured in the subgraph obtained by removing v — paths must not pass through v. Pairs unreachable in G \ {v} contribute 0.

local_scan_0

Local scan-0: vertex degree (unweighted) or strength (weighted).

local_scan_0_them

Local scan-0 on two graphs: degree/strength from them restricted to edges that also exist in us.

local_scan_1

For each vertex, count edges within its closed 1-neighborhood.

local_scan_1_ecount

Local scan-1 edge count / weight sum in the 1-neighbourhood of every vertex, with directed-mode support.

local_scan_1_ecount_them

Local scan-1 edge count on two graphs: count edges from them in the 1-neighbourhood defined by us.

local_scan_k

For each vertex, count edges within its closed k-neighborhood.

local_scan_k_ecount

Mode-aware local scan-k edge count / weight sum.

local_scan_k_ecount_them

Mode-aware local scan-k on two graphs.

local_scan_subset_ecount

Local scan on given vertex subsets: count edges (or sum weights) in the induced subgraph of each subset.

max_degree

Returns the maximum degree in the graph.

max_degree_vertex

Returns the vertex (or one of the vertices) with the maximum degree.

mean_degree

Mean degree of the graph.

mean_distance

Mean unweighted shortest-path length over all reachable ordered pairs. Counterpart of igraph_average_path_length(_, NULL_weights, _, _, /*directed=*/true, /*unconn=*/true).

mean_distance_weighted

Compute the weighted mean distance (average shortest path length).

min_degree

Returns the minimum degree in the graph.

neighborhood

k-hop neighbourhood vertex list for every vertex (mode = All, mindist = 0).

neighborhood_graphs

Per-vertex induced subgraphs of k-hop neighbourhoods (mode = All, mindist = 0).

neighborhood_graphs_with_mode

Per-vertex induced subgraphs of k-hop neighbourhoods with full mode control.

neighborhood_size

k-hop neighbourhood size for every vertex (mode = All, mindist = 0).

neighborhood_size_with_mode

Full mode-aware k-hop neighbourhood size with mindist filter.

neighborhood_with_mode

Full mode-aware k-hop neighbourhood vertex list with mindist filter.

pagerank

PageRank scores via power iteration with damping 0.85.

pagerank_linsys

PageRank via GMRES on (I - α · Mᵀ) · pr = (1 - α)/N · 1.

pagerank_weighted

Weighted PageRank scores via power iteration with damping 0.85.

personalized_pagerank

Personalized PageRank scores via power iteration.

personalized_pagerank_default

Personalized PageRank with default damping factor (0.85).

personalized_pagerank_vs

Personalized PageRank with a vertex-set reset distribution.

power_law_fit

Fit a power-law distribution to a sample of numbers.

reciprocity

Reciprocity of graph. Returns None for graphs with no edges (matches upstream’s IGRAPH_NAN).

reciprocity_with_mode

Reciprocity with explicit mode + ignore_loops (ALGO-PR-004b).

regularity

Return the regularity degree of the graph, or None if the graph is not regular.

rich_club_sequence

Per-vertex rich-club coefficient sequence for graph.

running_mean

Compute the running mean of a data vector.

satisfies_dirac

Check whether a graph satisfies Dirac’s condition.

satisfies_ore

Check whether a graph satisfies Ore’s condition.

similarity_dice

Compute the full Dice similarity matrix for all vertex pairs.

similarity_dice_es

Computes Dice similarity coefficients for pairs of vertices connected by the given edges.

similarity_dice_pairs

Computes Dice similarity coefficients for given vertex pairs.

similarity_inverse_log_weighted

Compute the full inverse-log-weighted (Adamic-Adar) similarity matrix.

similarity_inverse_log_weighted_pairs

Computes the inverse log-weighted (Adamic-Adar) similarity for given vertex pairs.

similarity_jaccard

Compute the full Jaccard similarity matrix for all vertex pairs.

similarity_jaccard_es

Computes Jaccard similarity coefficients for pairs of vertices connected by the given edges.

similarity_jaccard_pairs

Computes Jaccard similarity coefficients for given vertex pairs.

sort_vertices_by_degree

Return vertex IDs sorted by their degree.

strength

Weighted vertex degree for all vertices.

strength_with_mode

Weighted vertex degree with direction mode and loop control.

topological_sorting

Returns a topological ordering of graph’s vertices.

transitivity_avglocal_undirected

Average local transitivity (clustering coefficient).

transitivity_local_undirected

Local transitivity (clustering coefficient) per vertex.

transitivity_undirected

Global transitivity (clustering coefficient) of graph — 3 * triangles / connected_triples. Returns None when there are no connected triples (matches upstream’s IGRAPH_TRANSITIVITY_NAN mode); use .unwrap_or(0.0) for the IGRAPH_TRANSITIVITY_ZERO behaviour.

trussness

Compute the trussness of every edge in an undirected graph.

unfold_tree

Unfold a graph into a tree by BFS, replicating multiply-visited vertices.