Shortest-Path Multiplicity Heterogeneity as a Graph Diagnostic for Radial Organization in Sampled Geometries

@misc{ylla2026shortestpath,
  title = {{Shortest-Path Multiplicity Heterogeneity as a Graph Diagnostic for Radial Organization in Sampled Geometries}},
  author = {Ariadna Uxue Palomino Ylla},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.27248},
  eprint = {2606.27248},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.27248},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Shortest-Path Multiplicity Heterogeneity as a Graph Diagnostic for Radial Organization in Sampled Geometries
AU  - Ariadna Uxue Palomino Ylla
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2606.27248
UR  - https://arxiv.org/abs/2606.27248
AB  - Shortest-path counts describe how many minimal routes connect a pair of graph vertices, complementing distance alone. We study their heterogeneity within graph-distance shells using C_log(p, r_g), the cube root of the third absolute central moment of log shortest-path multiplicities. This permutation-invariant statistic measures variation across shell targets and does not encode direction by itself. In a Flamm--Schwarzschild case study, its radial profile differs from that of a matched-flat control. The binned statistic has a Pearson correlation of approximately 0.912 with a logarithmic Schwarzschild reference profile, indicating radial-reference agreement rather than reconstruction of continuum curvature. Comparisons across sample sizes and neighbor parameters further describe behavior under the tested graph constructions. Preserved summaries and plotting records support the numerical evidence, although original graph realizations and the definitive execution state were not recovered. These results motivate multiplicity heterogeneity as a graph diagnostic for radial organization, with interpretation conditional on sampling, connectivity and boundary effects.
ER  -