graph_physarum_path — GRAPH `flow` op

• Data kinds: matrix → table

• Call: import fullseye as fs; fs.ledger.graph_physarum_path(lengths, source=0, sink=None, dt=0.1, max_iters=5000, tol=1e-06, frac=0.5) (to call the implementation directly, import physarum_search; physarum_search.graph_physarum_path(lengths, source=0, sink=None, dt=0.1, max_iters=5000, tol=1e-06, frac=0.5); from the registry, opsgraph.get("graph_physarum_path"))

Usage

Shortest path by the slime mould's tube dynamics (Tero et al. 2010) on a weighted graph.

`lengths is a symmetric (n, n) matrix of tube lengths (0` = no tube, diagonal 0).

A unit flow is pushed from `source to sink (default n - 1`) through tubes of

conductance `D_e`; the pressures solve the weighted Laplacian (Kirchhoff), the flow in a

tube is `Q_e = D_e (p_u - p_v) / L_e, and each tube adapts dD_e/dt = |Q_e| - D_e`

(explicit Euler, step `dt`). Bonifaci, Mehlhorn and Varma (2012) prove that with a unique

shortest path the conductances converge to its indicator: `D_e -> 1 on it, 0` off it.

The path is read by following, from the source, the tube that carries the most flow out of

each node (a potential flow has no cycle); it must be at least `frac` of the thickest tube

all along, else the run is refused as not converged.

Returns `conductance and flow ((n, n) matrices, flow antisymmetric), path`

(node indices source → sink), `path_length` (sum of the tube lengths along it),

`flow_length = sum |Q_e| L_e (the length of the unit flow; it is >= path_length`

for every unit flow and equal only when all flow rides shortest paths), `iters`,

`converged (max |dD| fell below tol), history` (max |dD| per iteration).

Raises `ValueError`: matrix not square / symmetric / finite / non-negative, self-loops;

bad node indices or `source == sink; sink unreachable; dt` outside (0, 1]; no path

survived the threshold (not converged).

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_physarum_maze — py -3.11 examples/poc_physarum_maze.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 (`flow`)

physarum_route · graph_physarum_transport · physarum_transport_image

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

graph_physarum_path — GRAPH flow op