Percolation in anisotropic limited-degree networks
By: Jacopo Alexander Garofalo
From: Department of Mathematics and Physics, University of Campania “Luigi Vanvitelli”, Viale Lincoln 5, Caserta, 81100, Italy
At: Building C2, room 2.4.16
[2026-04-09]
Many real-world infrastructures, from sensor and road networks to power grids, are spatially embedded and anisotropic, with constraints on the maximum number of links each node can establish. Such systems can be represented as anisotropic limited-degree networks, in which each node forms at most q outgoing links preferentially oriented along a fixed direction.
By increasing the node density at fixed q, we uncover a reentrant percolation transition: a giant strongly connected component emerges, but unexpectedly disintegrates again at high densities. This counterintuitive behavior implies that adding nodes, normally expected to enhance robustness, can instead reduce mutual accessibility and weaken global connectivity. The critical behavior displays two coexisting phases: random-percolation scaling along the preferred direction and directed-percolation scaling transversely. These findings demonstrate that anisotropy and degree limitation can jointly induce a novel reentrant connectivity with mixed universality that bridges the universality classes of random and directed percolation, providing fresh insight into how structural constraints shape connectivity and resilience in spatial networks.