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

EigenvectorScores

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

HitsScores

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

Enums

CorenessMode

Direction-handling for coreness_with_mode.

EigenvectorMode

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

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.

Functions

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.

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_weighted

Per-vertex weighted betweenness centrality.

closeness

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

closeness_weighted

Per-vertex weighted closeness centrality.

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_triangles

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

density

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

edge_betweenness

Per-edge unweighted 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.

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_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.

hub_and_authority_scores

Compute Kleinberg’s hub and authority scores.

is_acyclic

Returns true iff graph contains no cycle.

is_complete

Returns true iff every pair of distinct vertices is adjacent.

is_dag

Returns true iff graph is a directed acyclic graph.

is_forest

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

is_loop

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

is_multiple

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

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_tree

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

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.

mean_distance

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

neighborhood

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

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_weighted

Weighted PageRank scores via power iteration with damping 0.85.

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).

topological_sorting

Returns a topological ordering of graph’s vertices.

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.