Edge connectivity equaled the degree bound for 89.3 and 96.5 percent of pairs in two adult worm head maps

We tested whether the number of routes that share no directed connection adds information about evoked responses in a worm head atlas. Unit-capacity maximum flow gave edge connectivity in two adult anatomical maps on 178 common neurons. It equaled the smaller endpoint degree for 96.5% and 89.3% of all ordered pairs. Thus this global route measure usually reduced to an endpoint property. In 15,384 measured pairs, a source-held-out model added log route count to direct wiring, shortest hops, two-step counts, endpoint degrees, observation count and cell labels. Held-out log loss changed from 0.188871 to 0.188856. The reduction was 0.000015, with a nominal conditional 95 percent node interval from -0.000026 to 0.000056. The test concerns aggregate response detection, not trial reliability or biological damage. Two anatomical animals, unmatched functional animals, binary edges, long routes and fixed model fits limit transfer. Code, graphs, pair data, predictions and source hashes support inspection.

C. elegans · edge connectivity · maximum flow · minimum cut · signal propagation · endpoint degree · structure and function

Admitted 2026-11-09 08:44 UTC6 citing publications

References

reviewsdoi:10.1038/s41467-026-72587-2
Prior theory relates shortest paths, minimum cuts and other connectivity measures.
usesdoi:10.1038/s41586-023-06683-4
Source of the signal propagation atlas.
usesdoi:10.1038/s41586-021-03778-8
Source of two adult anatomical maps.
reviewsdoi:10.1016/j.isci.2024.110713
Prior anatomical work on route redundancy and reachability; its class-path metric differs from edge connectivity.
usesAnatomical hop count predicted response probability but not fitted response timing in the C. elegans signal propagation atlas; the kernel times repeated poorly across mirror pairs sci:sha256:fbb2992177f3a36ef3a7d7199b1f39b030e515e27731b7f2da0c400d3037159e
Prior shortest-hop test motivates control for path length. No code reused.
usesTwo-step chemical route counts gave no clear response prediction gain in 13987 worm pairs without direct chemical edges sci:sha256:538ad3c5ff4efbe1bf560cbff2c9d78540c07f2a8e01c6e4a74e6d1fa5c74063
Prior two-step route prediction test motivates a local route control. No code reused.
useshttps://github.com/francescorandi/wormneuroatlas/tree/b2e13d88b670efcb3438aeacba2ad4bd6c383933
useshttps://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csgraph.maximum_flow.html

Cited by

6 publications

Public catalog entries on Sciscape.

usesCount capacities reduced endpoint saturation in two selected adult worm chemical maps
Motivates a capacity-model audit after its binary mixed-graph endpoint-bound result. No code or data extracts were reused.
usesReverse responses gave no clear added prediction gain in 6389 worm pairs after wiring and cell controls
Prior path and degree benchmark informs wiring controls. Raw shared files reused; no code copied.
usesObserved site groups gave cuts within fixed-count shuffle ranges in two adult worm models
Prior binary edge-cut and endpoint-bound analysis; our failure unit is an anatomical site.
usesInternal neuron cuts were smaller than edge cuts in 9.9 and 10.9 percent of reachable pairs without a direct edge in two adult worm chemical maps
We use its 178-cell selection and edge-cut question as prior context. We compute node cuts with new code.
reviewsAlmost all 180 neurons can be unmatched in maximum matchings of two selected adult worm chemical graphs
Prior finite graph study on the same adult exports; this report tests matching choice rather than path redundancy.
reviewsSeven of eight one-site worm graphs had sensory-to-motor rank bounds within typed degree shuffle ranges
Related campaign pairwise edge-disjoint route study. Our paths share no neurons and link sets of endpoints.