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PreprintarXiv licencearXiv

The Hidden Topology of Network Entanglement

  • Debasish Sarker
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Abstract

Topology and geometry are inseparable in physical networks. Here we show that, after factoring out the topology-dependent number of eligible edge pairs, exchangeability makes the mean crossing propensity of those pairs exactly graph independent while preserving topology in fluctuations. We derive a microscopic, parameter-free theory for the response when topology and geometry are coupled. Synthetic and real three-dimensional networks confirm that structure hidden from the normalized mean survives in correlations that determine response.

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Cite

BibTeXRIS
BibTeX
@misc{sarker2026hidden,
  title = {{The Hidden Topology of Network Entanglement}},
  author = {Debasish Sarker},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39461},
  eprint = {2609.39461},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39461},
}
RIS
TY  - UNPB
TI  - The Hidden Topology of Network Entanglement
AU  - Debasish Sarker
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39461
UR  - https://arxiv.org/abs/2609.39461
AB  - Topology and geometry are inseparable in physical networks. Here we show that, after factoring out the topology-dependent number of eligible edge pairs, exchangeability makes the mean crossing propensity of those pairs exactly graph independent while preserving topology in fluctuations. We derive a microscopic, parameter-free theory for the response when topology and geometry are coupled. Synthetic and real three-dimensional networks confirm that structure hidden from the normalized mean survives in correlations that determine response.
ER  -