null op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.graph_degree_preserving_null(adj, n_samples=20, swaps_per_edge=5, seed=0) (to call the implementation directly, import graphinv; graphinv.graph_degree_preserving_null(adj, n_samples=20, swaps_per_edge=5, seed=0); from the registry, opsgraph.get("graph_degree_preserving_null"))
Compare 3-cycles and reciprocity against a degree-preserving null model.
Each null sample requests swaps_per_edge * |E| edge swaps that keep every node's in- and out-degree exactly (Maslov & Sneppen 2002); a swap that would create a self-loop or duplicate edge is skipped, so dense graphs accept fewer (swaps_accepted). The sample's degree sequences are checked against the original before it is used — a null that drifted would make every ratio a lie, so this fails closed.
Returns a dict with the observed cycles3 and reciprocal_pairs, the null *_null_mean / *_null_sd, the *_ratio (observed / null mean) and *_z, plus n_samples, swaps (requested per sample) and swaps_accepted (list, accepted per sample). Ratios are what let graphs of different size be compared; raw counts cannot.
Raises ValueError: as graph_degree_summary; n_samples < 2 (no spread to estimate); swaps_per_edge < 1; a graph with fewer than 2 edges (nothing to swap).
• 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.
• graphinv_three_phyla — py -3.11 examples/graphinv_three_phyla.py
table as input)graph_edge_consensus · graph_core_persistence · tree_morphometry · tree_sholl · tree_run_length
null)—
*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.