Module properties

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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.
EccentricityClasses: Result of eccentricity_classes.
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.
GraphSummary: Result of graph_summary containing precomputed graph statistics.
HitsScores: Output of hub_and_authority_scores: scaled hub and authority vectors and the dominant eigenvalue of A·Aᵀ.
LabelSpreadResult: Result of label spreading prediction.
PowerLawFitResult: Result of fitting a power-law distribution to a sample.
StronglyRegularParams: Result of strongly regular graph recognition.
StructuralFeatures: Per-vertex structural feature vector.
UnfoldTreeResult: Result of unfolding a graph into a tree.

Enums§

AdjacencyType: Which triangle of the adjacency matrix to fill (undirected graphs only).
AggMode: Aggregation mode for neighborhood operations.
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§

abc_entropy: Compute the ABC entropy.
abc_index: Compute the atom-bond connectivity (ABC) index.
adjacency_spectral_gap_ratio: Compute the spectral gap ratio.
albertson_coindex: Compute the Albertson coindex.
albertson_index: Compute the Albertson index (edge irregularity).
algebraic_connectivity: Compute the algebraic connectivity of a graph.
are_adjacent: Check whether two vertices are connected by at least one edge.
arithmetic_geometric_index: Compute the arithmetic-geometric index.
articulation_ratio: Compute the articulation ratio.
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.
atom_bond_sum_connectivity: Compute the atom-bond sum-connectivity index.
attention_aggregate: Aggregate a signal with per-edge attention weights.
augmented_forman_ricci_curvature: Augmented Forman-Ricci curvature for each edge.
augmented_zagreb_index: Compute the augmented Zagreb index.
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).
average_path_resilience: Compute the average path resilience.
average_sombor_index: Compute the average Sombor index.
avg_local_clustering: Compute the average local clustering coefficient.
avg_nearest_neighbor_degree: Average nearest-neighbour degree, per vertex.
avg_neighbor_connectivity: Compute the average neighbor connectivity of the graph.
avg_neighbor_degree_ratio: Compute the average neighbor degree ratio.
avg_path_fraction: Compute the average path fraction.
balaban_j_index: Compute the Balaban J index of a graph.
bandwidth: Compute the exact graph bandwidth B(G).
bandwidth_lower_bound: Compute a lower bound on graph bandwidth.
bandwidth_of_labeling: Compute the bandwidth of a specific labeling.
bell_index: Compute the Bell index (degree population variance).
bertz_complexity_index: Compute the Bertz complexity index.
betweenness: Per-vertex (unweighted) betweenness centrality.
betweenness_centralization: Compute betweenness centralization.
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.
biconnected_ratio: Compute the biconnected ratio.
bipartiteness_ratio: Compute the bipartiteness ratio (2 - μ_n) / 2.
bipartivity_index: Compute the bipartivity index.
bottleneck_ratio: Compute the bottleneck ratio.
bridge_edge_ratio: Compute the bridge ratio.
bridge_ratio: Compute the bridge ratio of the graph.
centrality_correlation: Compute the centrality correlation (betweenness vs closeness).
centrality_divergence: Compute the Jensen-Shannon divergence between degree centrality and betweenness centrality distributions.
centrality_entropy: Compute the Shannon entropy of the degree centrality distribution.
centrality_rank_correlation: Compute the Spearman rank correlation between degree centrality and betweenness centrality.
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.
cheeger_bounds: Compute Cheeger constant bounds from the normalized Laplacian.
chromatic_number_greedy: Count the number of colors used in a coloring.
circuit_rank_ratio: Compute the circuit rank ratio of the graph.
class_homophily: Class-balanced homophily ratio (adjusted for class imbalance).
clique_cover_number: Compute the clique cover number θ(G).
closed_triplet_ratio: Compute the closed triplet ratio (global transitivity).
closeness: Per-vertex closeness centrality (Vec<Option<f64>>).
closeness_centralization: Compute closeness centralization.
closeness_cutoff: Range-limited closeness centrality.
closeness_weighted: Per-vertex weighted closeness centrality.
clustering_bimodality: Sarle’s bimodality coefficient of the clustering coefficient distribution.
clustering_degree_correlation: Compute the clustering-degree correlation.
clustering_entropy: Normalised Shannon entropy of the clustering coefficient distribution.
clustering_path_ratio: Compute the clustering-path ratio.
clustering_variance: Variance of local clustering coefficients.
cocitation: Computes the cocitation scores between all pairs of vertices.
collatz_sinogowitz: Compute the Collatz–Sinogowitz irregularity.
communicability_matrix: Compute the communicability matrix between all pairs of vertices.
community_size_balance: Compute the community size balance.
component_ratio: Compute the component ratio.
conductance: Compute the conductance of a partition.
connective_eccentricity_index: Compute the connective eccentricity index.
connectivity_index: Compute the connectivity index of the graph.
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.
core_density: Compute the core density.
core_periphery_gradient: Compute the core-periphery gradient.
core_persistence: Average coreness divided by the degeneracy (maximum coreness).
core_ratio: Compute the core ratio.
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_pairs_at_distance: Compute the number of vertex pairs at a given distance.
count_triangles: Count the number of triangles in graph. Edge directions, parallel edges, and self-loops are ignored.
cut_size: Compute the cut size of a partition.
cyclomatic_density: Compute the cyclomatic density.
degeneracy: Return the degeneracy of a graph.
degeneracy_gap: Degeneracy gap: (degeneracy − average_coreness) / degeneracy.
degree_assortativity_proxy: Compute the degree assortativity proxy.
degree_centralization: Compute degree centralization.
degree_closeness_correlation: Compute the degree-closeness correlation.
degree_concentration: Compute the degree concentration.
degree_core_ratio: Compute the core ratio (fraction of vertices with degree ≥ d̄).
degree_correlation_vector: Compute the degree correlation function k_nn(k).
degree_cv: Compute the degree coefficient of variation.
degree_density: Compute the degree density (normalized second moment of degree).
degree_diff_connectivity: Compute the degree difference connectivity index.
degree_distance: Compute the degree-distance index (Schultz-type).
degree_distance_correlation: Compute the degree-distance correlation.
degree_distribution: Compute the degree distribution histogram of a graph.
degree_diversity: Compute the degree diversity (number of distinct degree values).
degree_eccentricity_index: Compute the degree-eccentricity index.
degree_entropy: Shannon entropy of the degree distribution.
degree_entropy_ln: Compute the Shannon entropy of the degree distribution (natural log).
degree_entropy_normalized: Compute the normalized degree entropy.
degree_entropy_ratio: Compute the degree entropy ratio.
degree_gini: Compute the Gini coefficient of the degree sequence.
degree_harmonic_mean_index: Compute the degree harmonic mean index.
degree_herfindahl: Compute the Herfindahl–Hirschman index of the degree sequence.
degree_hierarchy: Compute the degree hierarchy (Gini coefficient of degrees).
degree_hoover: Compute the Hoover index (Robin Hood index) of the degree sequence.
degree_iqr: Compute the interquartile range (IQR) of the degree sequence.
degree_isolated_ratio: Compute the isolated ratio (fraction of degree-0 vertices).
degree_kurtosis: Compute the excess kurtosis of the degree distribution.
degree_laplacian_energy: Compute the degree Laplacian energy of the graph.
degree_leaf_ratio: Compute the leaf ratio (fraction of degree-1 vertices).
degree_mad: Compute the mean absolute deviation of the degree sequence.
degree_max_deviation: Compute the maximum degree deviation from the mean.
degree_median: Compute the median of the degree sequence.
degree_median_ad: Compute the median absolute deviation of the degree sequence.
degree_mixing_entropy: Compute the degree mixing entropy.
degree_mode: Compute the mode of the degree sequence.
degree_neighbor_correlation: Compute the degree-neighbor correlation.
degree_neighbor_max_sum: Compute the sum of maximum neighbor degrees.
degree_neighbor_min_sum: Compute the sum of minimum neighbor degrees.
degree_neighbor_range_sum: Compute the sum of neighbor degree ranges.
degree_neighbor_variance_sum: Compute the sum of neighbor degree variances.
degree_pair_concentration: Fraction of edges in the most common degree-pair class.
degree_palma: Compute the Palma ratio of the degree sequence.
degree_profile: Compute degree profile for each vertex: [deg, deg², log(deg+1)].
degree_range: Compute the range of the degree sequence.
degree_range_ratio: Compute the edge connectivity ratio.
degree_sequence: Returns the degree sequence of the graph.
degree_skewness: Compute the skewness of the degree distribution.
degree_span_ratio: Compute the degree span ratio.
degree_spectral_gap_estimate: Compute the degree-based spectral gap estimate.
degree_structural_info: Structural information content based on degree sequence.
degree_sum_index: Compute the degree-sum index.
degree_tail_ratio: Compute the tail ratio (fraction of vertices with degree ≥ 2·d̄).
degree_theil: Compute the Theil index (GE(1)) of the degree sequence.
degree_variance: Compute the variance of the degree sequence.
degree_variance_ratio: Compute the degree variance ratio.
density: Edge density of graph. Counterpart of igraph_density(_, NULL_weights, _, /*loops=*/false).
diameter_radius_ratio: Compute the diameter-radius ratio.
diameter_ratio: Compute the diameter ratio.
diameter_vulnerability: Compute the diameter vulnerability.
dirichlet_energy: Compute the Dirichlet energy of a signal on a graph.
distance_energy: Compute the distance energy E_D = Σ |λ_i(D)|.
distance_estrada_index: Compute the distance Estrada index DEE = Σ exp(λ_i(D)).
distance_gini: Gini coefficient of the pairwise distance distribution.
distance_kurtosis: Compute the distance kurtosis.
distance_skewness: Compute the distance skewness.
distance_spectral_radius: Compute the distance spectral radius ρ_D = λ_1(D).
distance_spectrum: Compute the distance spectrum, sorted in decreasing order.
diversity: Structural diversity index for all vertices in an undirected graph.
dominance_ratio: Compute the dominance ratio.
ecc: Compute the edge clustering coefficient for eids in graph.
eccentric_connectivity_index: Compute the eccentric connectivity index.
eccentric_distance_sum: Compute the eccentric-distance sum.
eccentricity_classes: Classify each vertex by its eccentricity class.
edge_adamic_adar_sum: Compute the sum of Adamic–Adar indices across all edges.
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>).
edge_common_neighbor_sum: Compute the sum of common neighbor counts across all edges.
edge_conn_ratio: Compute the edge connectivity ratio.
edge_connectivity_ratio: Compute the edge connectivity ratio.
edge_degree_cosine: Compute the cosine similarity of degree vectors across edges.
edge_degree_covariance: Compute the degree covariance across edges.
edge_degree_diff_ratio: Compute the degree difference ratio over edges.
edge_degree_discrepancy: Compute the normalized degree discrepancy across edges.
edge_degree_entropy: Shannon entropy of the edge degree-pair distribution.
edge_degree_geometric_sum: Compute the edge degree geometric sum.
edge_degree_harmonic_sum: Compute the edge degree harmonic sum.
edge_degree_log_product: Compute the edge degree log-product sum.
edge_degree_max_sum: Compute the edge degree max sum.
edge_degree_mean_sum: Compute the edge degree mean sum.
edge_degree_min_sum: Compute the edge degree min sum.
edge_degree_pearson: Compute the Pearson correlation of endpoint degrees across edges.
edge_degree_product_ratio: Compute the product-sum ratio index over edges.
edge_degree_ratio_sum: Compute the edge degree ratio sum.
edge_degree_rms: Compute the edge endpoint degree RMS.
edge_degree_sorensen: Compute the Sørensen edge degree index.
edge_distribution_entropy: Compute the edge distribution entropy.
edge_entropy: Shannon entropy of the edge-degree distribution.
edge_heterophily: Heterophily ratio: 1 - edge_homophily.
edge_homophily: Edge homophily ratio: fraction of edges connecting same-label vertices.
edge_inverse_degree_sum: Compute the inverse degree-sum index over edges.
edge_jaccard_sum: Compute the sum of Jaccard overlap coefficients across all edges.
edge_overlap_sum: Compute the sum of overlap coefficients across all edges.
edge_pi_index: Compute the edge-PI index.
edge_resilience: Compute edge resilience λ(G) / m.
edge_surplus_ratio: Compute the edge surplus ratio.
edge_szeged_index: Compute the edge-Szeged index.
edge_vertex_ratio: Compute the edge-vertex ratio.
edge_weight_balance: Normalised entropy of the edge degree-pair distribution.
effective_resistance: Compute the effective resistance between two vertices.
effective_resistance_matrix: Compute the effective resistance matrix for all pairs.
efficiency_ratio: Compute the efficiency ratio.
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.
elimination_ordering: Compute an elimination ordering using the min-degree heuristic.
elliptic_sombor_index: Compute the elliptic Sombor index.
energy_ratio: Compute the energy ratio.
estrada_index: Compute the Estrada index of a graph.
ev_degree_randic: Compute the ev-degree Randić index.
even_odd_walk_ratio: Compute the even-odd walk ratio.
expand_path_to_pairs: Expand a vertex path into consecutive pairs for edge lookup.
expansion: Compute the expansion (isoperimetric number) of a partition.
exponential_abc: Compute the exponential atom-bond connectivity index.
exponential_augmented_zagreb: Compute the exponential augmented Zagreb index.
exponential_first_zagreb: Compute the exponential first Zagreb index.
exponential_forgotten: Compute the exponential forgotten index.
exponential_ga: Compute the exponential geometric-arithmetic index.
exponential_inverse_degree: Compute the exponential inverse degree index.
exponential_randic: Compute the exponential Randić index.
exponential_sum_connectivity: Compute the exponential sum-connectivity index.
fiedler_vector: Compute the Fiedler vector of a graph.
fifth_ga_index: Compute the fifth geometric-arithmetic index.
first_ev_degree_zagreb: Compute the first ev-degree Zagreb index.
first_gourava_index: Compute the first Gourava index.
first_hyper_gourava_index: Compute the first hyper-Gourava index.
first_hyper_zagreb: Compute the first hyper-Zagreb index.
first_hyper_zagreb_coindex: Compute the first hyper-Zagreb coindex.
first_inverse_nirmala: Compute the first inverse Nirmala index.
first_leap_zagreb: Compute the first leap Zagreb index.
first_multiplicative_zagreb: Compute the first multiplicative Zagreb index.
first_neighborhood_zagreb: Compute the first neighborhood Zagreb index.
first_redefined_zagreb: Compute the first redefined Zagreb index.
first_reformulated_zagreb: Compute the first reformulated Zagreb index.
first_transmission_zagreb: Compute the first transmission Zagreb index.
first_ve_degree_zagreb_alpha: Compute the first ve-degree Zagreb alpha index.
first_ve_degree_zagreb_beta: Compute the first ve-degree Zagreb beta index.
first_zagreb_coindex: Compute the first Zagreb coindex.
first_zagreb_connection: Compute the first Zagreb connection index.
first_zagreb_entropy: Compute the first Zagreb entropy.
first_zagreb_index: Compute the first Zagreb index M₁(G) = Σ deg(v)².
flow_hierarchy_ratio: Compute the flow hierarchy ratio.
forgotten_coindex: Compute the forgotten coindex (F-coindex).
forgotten_index: Compute the forgotten topological index.
forman_ricci_curvature: Forman-Ricci curvature for each edge.
fourth_abc_index: Compute the fourth atom-bond connectivity index.
freeman_degree_centralization: Compute Freeman’s degree centralization.
frustration_ratio: Compute the frustration ratio.
general_randic_index: Compute the general Randić index R_α(G).
general_sum_connectivity_index: Compute the general sum-connectivity index χ_α(G).
general_zeroth_order_randic: Compute the general zeroth-order Randić index.
geometric_arithmetic_index: Compute the geometric-arithmetic index.
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.
giant_component_gap: Compute the giant component gap.
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.
gordon_scantlebury_index: Compute the Gordon-Scantlebury index (path-of-length-2 count).
graovac_ghorbani_index: Compute the Graovac-Ghorbani index.
graph_compactness: Compute the compactness of the graph.
graph_energy: Compute the graph energy.
graph_integrity: Compute the integrity of a graph.
graph_periphery: Return the periphery vertices of a graph.
graph_summary: Compute a quick structural summary of a graph.
graph_summary_string: Format a detailed multi-line summary of a graph.
graph_toughness: Compute the toughness of a graph.
greedy_clique_cover: Find a greedy clique cover.
greedy_clique_number: Compute the greedy clique number (lower bound on chromatic number).
greedy_coloring: Greedy vertex coloring in natural vertex order.
greedy_coloring_largest_first: Greedy coloring with largest-first (LF) ordering.
greedy_coloring_with_order: Greedy vertex coloring with a custom vertex processing order.
greedy_independent_set: Find a maximal independent set using a greedy heuristic.
greedy_matching: Find a greedy maximal matching.
gutman_index: Compute the Gutman index.
hamiltonian_cycle: Find a Hamiltonian cycle using backtracking.
hamiltonian_path: Find a Hamiltonian path using backtracking.
harary_index: Compute the Harary index of a graph.
harmonic_centrality: Per-vertex harmonic centrality.
harmonic_centrality_cutoff: Range-limited harmonic centrality.
harmonic_centrality_weighted: Per-vertex weighted harmonic centrality.
harmonic_graph_index: Compute the harmonic index.
has_hamiltonian_cycle: Check whether a graph has a Hamiltonian cycle.
has_hamiltonian_path: Check whether a graph has a Hamiltonian path.
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.
heat_kernel_diffuse: Diffuse a signal on the graph using the heat kernel.
hop_entropy: Normalised Shannon entropy of the hop-distance distribution.
hosoya_index: Compute the Hosoya index (Z-index) of a graph.
hub_and_authority_scores: Compute Kleinberg’s hub and authority scores.
hub_dominance: Compute the hub dominance.
hub_dominance_ratio: Compute the hub dominance ratio.
hub_ratio: Compute the hub ratio.
hyper_wiener_index: Compute the hyper-Wiener index of a graph.
hyperbolicity: Compute δ-hyperbolicity as a floating-point value.
hyperbolicity_twice: Compute the Gromov δ-hyperbolicity of a graph.
independence_ratio: Compute the independence ratio α(G) / n.
independent_set_count_sequence: Compute the independence polynomial coefficient sequence.
inter_community_edge_ratio: Compute the inter-community edge ratio.
inverse_degree_index: Compute the inverse degree index (zeroth-order Randić index).
inverse_degree_power: Compute the inverse degree power index.
inverse_sum_indeg_index: Compute the inverse sum indeg index.
ira_index: Compute the power-difference irregularity index.
irb_index: Compute the root-difference irregularity index.
ird_index: Compute the square-difference irregularity index.
irga_index: Compute the geometric-arithmetic irregularity index.
irl_irregularity: Compute the IRL irregularity (irregularity by logarithm).
irlu_irregularity: Compute the IRLU irregularity (irregularity by log-ratio).
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_clique_cover: Check whether a partition of vertices forms a valid clique cover.
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_hamiltonian_cycle: Check whether a sequence of vertices forms a valid Hamiltonian cycle.
is_hamiltonian_path: Check whether a sequence of vertices forms a valid Hamiltonian path.
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_perfect_matching: Check whether a matching is a perfect matching.
is_planar: Test whether a graph is planar.
is_proper_coloring: Check whether a coloring is valid (proper).
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_valid_matching: Check whether a matching is valid.
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.
isolated_vertex_ratio: Compute the isolated vertex ratio.
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).
kirchhoff_index: Compute the Kirchhoff index of a graph.
kirchhoff_index_ratio: Compute the Kirchhoff index ratio.
label_propagate_predict: Predict labels using simple majority voting from labeled neighbors.
label_spread: Predict labels for unlabeled vertices using label spreading.
lanzhou_index: Compute the Lanzhou index.
laplacian_spectrum: Compute all Laplacian eigenvalues, sorted in ascending order.
largest_component_fraction: Compute the largest component fraction.
layer_ratio: Compute the layer ratio.
leaf_ratio: Compute the leaf ratio.
leaf_to_hub_ratio: Compute the leaf-to-hub ratio.
link_pred_adamic_adar: Compute Adamic-Adar Index for given vertex pairs.
link_pred_common_neighbors: Compute Common Neighbors score for given vertex pairs.
link_pred_jaccard: Compute Jaccard Coefficient for given vertex pairs.
link_pred_preferential_attachment: Compute Preferential Attachment score for given vertex pairs.
link_pred_resource_allocation: Compute Resource Allocation Index for given vertex pairs.
list_triangles: List all triangles in a graph.
local_density_ratio: Compute the local density ratio.
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_efficiency_ratio: Compute the local efficiency ratio.
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.
matching_count_sequence: Compute the matching count sequence [m(G,0), m(G,1), …].
matching_number: Compute the matching number ν(G).
max_degree: Returns the maximum degree in the graph.
max_degree_vertex: Returns the vertex (or one of the vertices) with the maximum degree.
max_flow_efficiency: Compute the max-flow efficiency ratio.
maximum_matching: Find the maximum matching (brute-force).
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).
mean_eccentricity_ratio: Compute the mean eccentricity ratio.
mean_forman_ricci: Compute the average Forman-Ricci curvature of the graph.
merrifield_simmons_index: Compute the Merrifield–Simmons index of a graph.
meshedness_coefficient: Compute the meshedness coefficient of the graph.
min_degree: Returns the minimum degree in the graph.
min_degree_connectivity_ratio: Compute the vertex connectivity ratio.
minmax_degree_ratio: Compute the min-max degree ratio index.
modified_first_zagreb: Compute the modified first Zagreb index.
modified_first_zagreb_connection: Compute the modified first Zagreb connection index.
modified_sombor_index: Compute the modified Sombor index.
modularity_upper_bound_ratio: Compute the modularity upper bound ratio.
mostar_index: Compute the Mostar index of a graph.
multi_edge_ratio: Compute the multi-edge ratio of the graph.
multiplicative_abc: Compute the multiplicative atom-bond connectivity index.
multiplicative_ga: Compute the multiplicative geometric-arithmetic index.
multiplicative_randic: Compute the multiplicative Randić index.
multiplicative_sum_connectivity: Compute the multiplicative sum-connectivity index.
multiplicatively_weighted_harary: Compute the multiplicatively weighted Harary index.
narumi_katayama_index: Compute the Narumi-Katayama index.
natural_connectivity: Compute the natural connectivity of a graph.
navigability_ratio: Compute the navigability ratio.
neighbor_aggregate: Aggregate a signal over each vertex’s neighborhood.
neighbor_connectivity_ratio: Compute the neighbor connectivity ratio.
neighbor_degree_disparity: Compute the average neighbor degree ratio.
neighborhood: k-hop neighbourhood vertex list for every vertex (mode = All, mindist = 0).
neighborhood_forgotten_index: Compute the neighborhood forgotten index.
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.
nirmala_index: Compute the Nirmala index.
node_homophily: Node homophily ratio: average proportion of same-label neighbors.
normalized_algebraic_connectivity: Compute the normalized algebraic connectivity μ_2(L_norm).
normalized_cut: Compute the normalized cut (NCut) of a partition.
normalized_dirichlet_energy: Compute the normalized Dirichlet energy (Rayleigh quotient form).
normalized_laplacian_spectrum: Compute the normalized Laplacian spectrum, sorted ascending.
odd_cycle_density: Compute the odd cycle density.
ollivier_ricci_curvature: Ollivier-Ricci curvature for each edge (lazy random walk variant).
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.
pendant_edge_ratio: Compute the pendant edge ratio.
periphery_fraction: Compute the periphery fraction.
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.
pi_index: Compute the Padmakar-Ivan (PI) index of a graph.
platt_index: Compute the Platt index (sum of edge degrees).
power_law_fit: Fit a power-law distribution to a sample of numbers.
ppr_diffuse: Diffuse a signal using Personalized PageRank propagation.
randic_entropy: Compute the Randić entropy.
randic_index: Compute the Randić connectivity index.
ratio_cut: Compute the ratio cut of a partition.
reach_decay: Average fraction of vertices reachable within half the diameter.
reciprocal_degree_distance: Compute the reciprocal degree distance (additively weighted Harary index).
reciprocal_randic_index: Compute the reciprocal Randić index.
reciprocal_transmission_index: Compute the reciprocal transmission index.
reciprocity: Reciprocity of graph. Returns None for graphs with no edges (matches upstream’s IGRAPH_NAN).
reciprocity_ratio: Compute the reciprocity ratio of the graph.
reciprocity_with_mode: Reciprocity with explicit mode + ignore_loops (ALGO-PR-004b).
reduced_first_zagreb: Compute the reduced first Zagreb index.
reduced_forgotten_index: Compute the reduced forgotten index.
reduced_reciprocal_randic: Compute the reduced reciprocal Randić index.
reduced_second_zagreb: Compute the reduced second Zagreb index.
reduced_sombor_index: Compute the reduced Sombor index.
reduced_sum_connectivity: Compute the reduced sum-connectivity index.
regularity: Return the regularity degree of the graph, or None if the graph is not regular.
resistance_centrality: Compute resistance centrality for all vertices.
resistance_regularity: Compute the resistance regularity ratio.
revised_szeged_index: Compute the revised Szeged index of a graph.
rich_club_density: Compute the rich club density.
rich_club_sequence: Per-vertex rich-club coefficient sequence for graph.
running_mean: Compute the running mean of a data vector.
rwpe: Compute Random Walk Positional Encoding for all vertices.
rwpe_vertices: Compute RWPE only for specified vertices (more efficient for batches).
satisfies_dirac: Check whether a graph satisfies Dirac’s condition.
satisfies_ore: Check whether a graph satisfies Ore’s condition.
schultz_index: Compute the Schultz index (degree-distance index).
second_ev_degree_zagreb: Compute the second ev-degree Zagreb index.
second_gourava_index: Compute the second Gourava index.
second_hyper_zagreb: Compute the second hyper-Zagreb index.
second_hyper_zagreb_coindex: Compute the second hyper-Zagreb coindex.
second_inverse_nirmala: Compute the second inverse Nirmala index.
second_leap_zagreb: Compute the second leap Zagreb index.
second_multiplicative_zagreb: Compute the second multiplicative Zagreb index.
second_neighborhood_zagreb: Compute the second neighborhood Zagreb index.
second_reformulated_zagreb: Compute the second reformulated Zagreb index.
second_transmission_zagreb: Compute the second transmission Zagreb index.
second_ve_degree_zagreb: Compute the second ve-degree Zagreb index.
second_zagreb_coindex: Compute the second Zagreb coindex.
second_zagreb_connection: Compute the second Zagreb connection index.
second_zagreb_entropy: Compute the second Zagreb entropy.
second_zagreb_index: Compute the second Zagreb index M₂(G) = Σ_{(u,v)∈E} deg(u)·deg(v).
self_loop_ratio: Compute the self-loop ratio of the graph.
shell_diversity: Shannon entropy of the k-shell size distribution, normalised to [0, 1].
sigma_coindex: Compute the sigma coindex.
sigma_index: Compute the sigma index (Gutman irregularity).
signless_laplacian_energy: Compute the signless Laplacian energy.
signless_laplacian_smallest: Compute the smallest signless Laplacian eigenvalue q_1(Q).
signless_laplacian_spectral_radius: Compute the signless Laplacian spectral radius q_n(Q).
signless_laplacian_spectrum: Compute the signless Laplacian spectrum, sorted ascending.
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.
smallworld_omega: Compute the small-world omega estimate.
smallworld_sigma: Compute the small-world sigma estimate.
smoothness_ratio: Compute the smoothness ratio of a signal on a graph.
sombor_coindex: Compute the Sombor coindex.
sombor_index: Compute the Sombor index.
sort_vertices_by_degree: Return vertex IDs sorted by their degree.
spanning_tree_count: Count the number of spanning trees using Kirchhoff’s theorem.
spanning_tree_ratio: Compute the spanning tree ratio.
spectral_bisection: Compute a spectral bisection of the graph.
spectral_gap: Compute the spectral gap of a graph.
spectral_gap_ratio: Compute the spectral gap ratio μ_2 / μ_n.
spectral_radius: Compute the spectral radius of a graph.
spectral_radius_ratio: Compute the spectral radius ratio.
square_clustering_ratio: Compute the square clustering ratio.
square_density: Compute the square (4-cycle) density of the graph.
strength: Weighted vertex degree for all vertices.
strength_with_mode: Weighted vertex degree with direction mode and loop control.
structural_feature_vectors: Compute structural feature vectors for all vertices.
structural_information_content: Compute the structural information content.
subgraph_centrality: Compute subgraph centrality for all vertices.
sum_connectivity_index: Compute the sum-connectivity index.
symmetric_degree_ratio: Compute the symmetric degree ratio index.
symmetric_diffuse: Diffuse a signal using symmetric normalized propagation.
symmetric_division_deg_index: Compute the symmetric division deg index.
szeged_index: Compute the Szeged index of a graph.
terminal_wiener_index: Compute the terminal Wiener index.
third_leap_zagreb: Compute the third leap Zagreb index.
third_zagreb_index: Compute the third Zagreb index.
topological_sorting: Returns a topological ordering of graph’s vertices.
total_eccentricity: Compute the total eccentricity.
total_irregularity: Compute the total irregularity.
total_variation: Compute the total variation of a signal on a graph.
transitivity_avglocal_undirected: Average local transitivity (clustering coefficient).
transitivity_gap: Compute the transitivity gap.
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.
transmission_ratio: Compute the transmission ratio.
treewidth_min_fill: Compute an upper bound on treewidth via min-fill elimination.
treewidth_upper_bound: Compute an upper bound on treewidth via min-degree elimination.
triangle_density: Compute the triangle density of the graph.
triangle_participation: Compute the triangle participation ratio.
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.
variable_first_zagreb: Compute the variable first Zagreb index.
variable_sum_exdeg: Compute the variable sum exdeg index.
vertex_conn_ratio: Compute the vertex connectivity ratio.
vertex_connectivity_ratio: Compute the vertex connectivity ratio.
vertex_resilience: Compute vertex resilience κ(G) / n.
von_neumann_entropy: Approximate Von Neumann entropy of the graph.
walk_entropy: Compute the walk entropy of the graph.
walk_regularity: Compute the walk regularity index of the graph.
wiener_index: Compute the Wiener index of a connected graph.
wiener_polarity_index: Compute the Wiener polarity index of a graph.

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