graph_modularity — CONNGRAPH stats op

• Data kinds: conn_graph × labels → measurement

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

Usage

Directed, weighted modularity Q (Leicht–Newman 2008).

Q = (1/m) Σ_ij (W_ij − k_i^out k_j^in / m) δ(c_i, c_j), m = Σ W. If all nodes are in 1 group, it is exactly 0. The diagonal (self-loops) is dropped. Weights must be non-negative.

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 measurement as input)

—

Same category (stats)

graph_degree_table · graph_clustering_coefficient · graph_betweenness · graph_laplacian_spectrum · graph_spectral_radius · graph_components · 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).*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.