Evidence for a Functional Proximity Law in Multilayer Networks

TL;DR

This study introduces the Functional Proximity Law in multilayer networks, showing hub importance scores are more persistent between functionally similar layers across diverse domains, validated through extensive experiments.

Contribution

The paper provides empirical evidence for a new law in multilayer networks, with broad validation and insights into structural conditions affecting its applicability.

Findings

Hub importance scores are more persistent in functionally similar layers.

The law is confirmed in 9 out of 12 canonical domains.

External validation on C. elegans connectome shows strong correlation (r=0.777).

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 17 pre-registered experiments: 12 canonical domains (9 confirmed, 3 denied; molecular biology, neuroscience, computer systems, ecology, linguistics) plus 5 external validations on independently-authored datasets. Eight canonical domains reach p < 0.05 individually; the directional inequality holds in all 9 confirmed. Three 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 14/17 pre-registered confirmations by chance: p ~ 0.006. The law is falsifiable, makes testable directional predictions, and identifies the structural conditions under which it fails.