Janus Percolation in Anisotropic Limited-Degree Networks

Abstract

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 sigma 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 "faces": random-percolation scaling along the preferred direction and directed-percolation scaling transversely, therefore we name this phenomenon Janus percolation, in analogy with the dual-faced Roman god. 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.

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