graph_betweenness — CONNGRAPH `stats` op

• Data kinds: conn_graph → signal

• Call: import fullseye as fs; fs.ledger.graph_betweenness(W: 'Any') -> 'np.ndarray' (to call the implementation directly, import conngraph; conngraph.graph_betweenness(W: 'Any') -> 'np.ndarray'; from the registry, opsconngraph.get("graph_betweenness"))

Usage

Betweenness centrality (Brandes 2001, binary directed, unnormalised). An array of length n, one value per node.

Value of node v = Σ_{s≠v≠t} σ_st(v) / σ_st (ratio of shortest-path counts). If the binary structure is symmetric (every edge is reciprocal), it is treated as an undirected graph: (s, t) and (t, s) count as 1 pair and the total is divided by 2 -- the textbook values where the centre of an undirected star (n nodes) gets (n−1)(n−2)/2 and the leaves get 0. If directed (asymmetric), ordered pairs are counted as they are.

Detailed usage guide

• conngraph family guide

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• (none yet)

Ops the type connects to (they accept `signal` as input)

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Same category (`stats`)

graph_degree_table · graph_clustering_coefficient · graph_laplacian_spectrum · graph_spectral_radius · graph_components · graph_modularity · graph_rich_club · graph_motif_count

*Provenance: conngraph.py — CONNGRAPH operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

graph_betweenness — CONNGRAPH stats op