Year: 2026
Type: preprint
Abstract: Complex networks balance metric wiring costs against functional routing demands, rarely conforming to idealized dichotomies of pure planar grids or unconstrained topologies. Yet, existing latent-space models remain computationally bottlenecked by stochastic sampling on small, unweighted graphs. Here, we formulate a scalable generative framework to solve the inverse problem of spatio-functional inference in weighted networks. By coupling explicit metric spaces with an unobserved latent geometry, we jointly reconstruct hidden coordinates and infer a coupling parameter $λ\in [0, 1]$, quantifying the connectivity propensity explained by functional affinity conditioned on metric distance decay. Our deterministic pipeline pairs a physics-informed spectral residual initialization with hybrid first- and quasi-Newton optimization. Across diverse empirical systems, the framework reveals a continuous spatio-functional spectrum. In the Drosophila melanogaster whole-brain connectome, it resolves an architectural progression from metric-constrained sensory circuits to specialized associative and chemo-affinity neuropils. In the continental European power grid, line pruning preserves a strictly metric baseline ($\hatλ \approx 0$), whereas topological rewiring drives a sharp surge in $\hatλ$, demonstrating that macroscopic component connectivity can mask spatial degradation. Finally, tracking global aviation throughout the COVID-19 pandemic captures dynamic regime shifts toward localized metric connectivity, establishing a unified diagnostic to probe structural organization and resilience in spatially embedded networks.
Source: arXiv (Cornell University)
Authors: Cerioli, Gabriele, Cerioli, Adamo
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214012965