graph_core_persistence — GRAPH `population` op

• Data kinds: table → table

• Call: import fullseye as fs; fs.ledger.graph_core_persistence(adjs, mode='in', weighted=False) (to call the implementation directly, import graphinv; graphinv.graph_core_persistence(adjs, mode='in', weighted=False); from the registry, opsgraph.get("graph_core_persistence"))

Usage

Which nodes sit in the innermost core of every individual — K wirings on one node order.

`adjs is a list of K square matrices or a table {name: matrix}` on the same

node order (a node absent from an individual is a zero row and column). For each

individual the innermost core of :func:graph_kcore (same `mode / weighted`) is

taken; `appearances[v]` counts the individuals whose innermost core contains v.

Following Yadav & Singh 2026, a node is persistent if it is in the core of all K,

recurrent if in 2 .. K−1, transient if in exactly 1, and never otherwise.

Returns a dict: `k (K), n, names, membership` (K, n) bool,

`appearances (n,), persistent / recurrent / transient / never` (n,)

bool masks, `n_persistent .. n_never, kmax` (K,) the innermost index per

individual, `n_inner (K,), mode, weighted`.

Identities: `sum(n_inner) == sum(appearances)`; the four classes partition the

nodes; K identical inputs make every core node persistent and nothing recurrent or

transient; every persistent node is in every individual's innermost core.

Raises `ValueError: adjs` not a list / table; fewer than 2 individuals;

matrices of different sizes; any refusal of :func:graph_kcore.

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)

• poc_worm_core_persists — py -3.11 examples/poc_worm_core_persists.py

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

graph_edge_consensus · tree_morphometry · tree_sholl · tree_run_length

Same category (`population`)

graph_edge_consensus · graph_strength_growth

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

graph_core_persistence — GRAPH population op