Module analysis 

The pure-algorithm graph analysis toolbox (centrality / community / pathfinding / cycles / components / k-core / similarity) — the compute core of the graph-DB IDE. Index-based (n, edges); no egui, no GPU. Graph analysis — the pure-algorithm core of the graph-DB IDE (V.G / G.V()).

Every algorithm works on the index-based representation (n, edges) — n nodes numbered 0..n and edges: &[(usize, usize)] (directed from → to) — the same shape crate::community::louvain already uses, so a caller maps its GraphModel (String ids) to indices once and runs the whole toolbox. Results are plain Vecs keyed by node index. No egui, no GPU, no RNG — deterministic and headless-testable.

Groups:

• [centrality] — degree / betweenness / closeness / pagerank / eigenvector.
• community — Louvain (re-exported) + label propagation.
• [pathfinding] — BFS / DFS / shortest path / all simple paths.
• [cycles] — cycle detection + topological sort.
• [components] — connected (undirected) + strongly-connected (Tarjan).
• [kcore] — k-core decomposition (core numbers).
• [similarity] — Jaccard / common-neighbours / Adamic–Adar / cosine.
• [stats] — whole-graph clustering coefficient + diameter / average path length.

Modules

centrality

Centrality — who matters in the graph, five ways. All return a Vec<f32> indexed by node (0..n). Deterministic; no RNG.

community

Community detection — the analysis-toolbox front door. Louvain modularity optimisation is re-exported from crate::community (the existing, well-tested implementation that drives the semantic-zoom meta-graph); label propagation is added here as a fast near-linear alternative.

components

Connected components — undirected (union-find) + strongly-connected (Tarjan, directed). Both return a labelling Vec<usize> (comp[i] = component id, compact 0..count) plus the component count.

cycles

Cycles & ordering — directed cycle detection, a topological sort (Kahn), and elementary-cycle enumeration (Johnson-style, bounded). Directed, over the out view.

kcore

k-core decomposition — each node’s core number: the largest k such that the node survives repeatedly peeling away every node of undirected degree < k. High core numbers mark the dense, well-connected heart of the graph.

pathfinding

Pathfinding — BFS / DFS orders, shortest paths (unweighted BFS + weighted Dijkstra), and all simple paths between two nodes. Directed (over the out view); pass an Adjacency built from undirected-doubled edges for undirected search.

similarity

Node similarity — neighbourhood-overlap measures over the undirected view: common neighbours, Jaccard, Adamic–Adar, and cosine. Each compares two nodes by how much their neighbour sets overlap — the link-prediction / “you may also know” primitive.

stats

Whole-graph statistics — the scalar summaries a stats panel shows, computed on the undirected view: the clustering coefficient (how tightly neighbourhoods close into triangles) and the diameter / average path length (the graph’s reach). These fill the two gaps the rest of super left open.

Structs

Adjacency

A built adjacency over n indexed nodes: directed out / in neighbour lists plus an undirected view, each carrying an edge weight (1.0 for unweighted input). Built once from (n, edges) and shared by the analysis algorithms.