The Functional Proximity Law: Hub Centrality Preservation in Multilayer Networks Across Domains
Abstract
We propose and empirically test the Functional Proximity Law: in any multilayer network, degree-centrality hub scores correlate more strongly between layers encoding functionally similar relationships than between layers encoding dissimilar ones. This holds across domains, independently of network size, layer definition, or data origin. We test the law across 23 independent domains spanning biology, engineering, linguistics, physics, neuroscience, and social science. 16 domains confirm the law. 7 are denied — each denial receives a distinct, named mechanistic explanation (resolution mismatch, institutional operating model, adversarial construction). All hypotheses are pre-registered via SHA-256 hash + UTC timestamp before each experiment run, proving predictions preceded results. All experiments are reproducible with IRDME, a zero-external-dependency pure Python 3 tool.
Confirmed Domains (16)
| Domain | n | r similar | r dissim. | p |
|---|---|---|---|---|
| CPU Block Design | 10 | +0.6217 | −0.6490 | 0.030 |
| Cytokine Cascade Network | 18 | +0.5122 | −0.4082 | — |
| East African Savanna Food Web (v1) | 15 | +0.4262 | −0.1213 | 0.116 |
| East African Savanna Food Web (v2) | 15 | +0.5586 | −0.0647 | 0.034 |
| English Lexical Network | 20 | +0.2759 | −0.7477 | 0.241 |
| European City Road Network | 10 | — | — | — |
| Full Periodic Table of Elements | 118 | — | — | — |
| Global Internet AS Topology | 18 | +0.5160 | −0.2671 | 0.026 |
| Global Supply Chain | 14 | — | — | — |
| Human Brain Connectome | 16 | +0.7029 | +0.1780 | 0.004 |
| IRDME Codebase (v1.1) | 14 | +0.9411 | −0.3037 | 0.283 |
| Linux Kernel Architecture (v6.x) | 30 | +0.7028 | −0.1452 | 0.002 |
| p53 DNA Damage Response | 15 | — | — | — |
| p53 Network — 4-Layer | 15 | +0.9276 | +0.7321 | 0.012 |
| p53 Network — STRING v12 | 15 | +0.9729 | −0.1613 | 0.643 |
| Social Trust Network | 15 | — | — | — |
p = two-tailed permutation test (200 shuffles, seed=42). — = not stored or not applicable. CONFIRMED = r(similar) > r(dissimilar), pre-registered.
Boundary Conditions — Denied Domains (7)
Denied results are discoveries, not failures. Each reveals a named constraint on the law.
Methodology
For each multilayer graph G = (V, E₁…Eₖ), degree centrality d_i(v) is computed per layer i and item v. Pearson r is computed between d_i and d_j for all layer pairs. Spearman r is used as a robustness check (introduced v4.4, all confirmed domains show sign agreement). A permutation test shuffles item labels 200 times to generate an empirical p-value.
Layer pairs are classified as similar or dissimilar a priori, before running experiments, via pre-registration. Pre-registration uses SHA-256[:16] hashes of hypothesis statements + UTC timestamps, stored as sidecar files alongside every experiment JSON. This creates a public log of predictions with git timestamps — a history and audit trail, not a cryptographic proof against private prior analysis.
CONFIRMED = r(similar) > r(dissimilar). This is the directional test. Statistical significance (p < 0.05) is achieved in 6 of 16 confirmed domains; the remaining 10 confirm the directional law without reaching significance, consistent with small-n designs (n = 9–118).
Pre-registration & Reproducibility
All experiment files include SHA-256-hashed, UTC-timestamped hypothesis statements committed before each run. To reproduce: python main.py <experiment.json> output.json. Pre-registration repository (experiment files + hashes): github.com/vladi160/the-beginning. The IRDME engine itself is closed-source; the pre-registration record and all experiment configs are public.