Evidence for a Functional Proximity Law in Multilayer Networks
Abstract
Hub importance scores in multilayer networks persist more strongly between functionally similar layers than dissimilar ones. We call this the Functional Proximity Law and test it across 23 pre-registered experiments: 13 canonical domains (10 confirmed, 3 denied; molecular biology, neuroscience, computer systems, ecology, linguistics, AI architecture) plus 10 pre-registered external validations (9 confirmed, 1 denied). Nine canonical domains reach p < 0.05 individually; the directional inequality holds in all 10 confirmed. Four DENIED domains reveal named structural boundary conditions that narrow the law's scope. A fully external validation on the C. elegans connectome, where both data and layer definitions are independent of the authors, yields r = 0.777 (p = 0.004). Binomial probability of 19/23 pre-registered confirmations by chance: p approx. 0.0013 (p < 0.002). The law is falsifiable, makes testable directional predictions, and identifies the structural conditions under which it fails.
Keywords
Cite
@article{arxiv.2604.23639,
title = {Evidence for a Functional Proximity Law in Multilayer Networks},
author = {Vladi Ivanov},
journal= {arXiv preprint arXiv:2604.23639},
year = {2026}
}
Comments
23 pages, 5 tables. v2 extends v1 from 17 to 23 pre-registered experiments: 19/23 confirmations, p approx. 0.0013. Adds external validations, new boundary conditions, and corrected claim scope. Pre-registration records: https://github.com/vladi160/preregistrations. Zenodo: https://doi.org/10.5281/zenodo.20349791