graph_degree_summary — GRAPH degree op

• Data kinds: matrix → table

• Call: import fullseye as fs; fs.ledger.graph_degree_summary(adj) (to call the implementation directly, import graphinv; graphinv.graph_degree_summary(adj); from the registry, opsgraph.get("graph_degree_summary"))

Usage

Degrees, density and reciprocity of a directed wiring matrix.

adj is a square matrix; entry (i, j) > 0 means an edge i -> j. Self-loops are counted separately and excluded from the edge statistics. Returns a dict with n, edges, self_loops, the in_degree / out_degree arrays, density (edges / (n (n-1))), and reciprocal_pairs (unordered pairs wired in both directions).

The identity in_degree.sum() == out_degree.sum() == edges holds exactly for any directed graph and is checked before returning (fail-closed — if it ever broke, the matrix was not what the caller thought).

Raises ValueError: non-square / empty / non-finite / negative input, or a matrix over the node cap.

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)

• graphinv_three_phyla — py -3.11 examples/graphinv_three_phyla.py

• poc_connectome_lr_symmetry — py -3.11 examples/poc_connectome_lr_symmetry.py

Ops the type connects to (they accept table as input)

graph_edge_consensus · graph_core_persistence · tree_morphometry · tree_sholl · tree_run_length

Same category (degree)

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*Provenance: graphinv.py — GRAPH 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.