Multi-Universality and Localized Attacks in Spatially Embedded Networks

We study a realistic spatial network model constructed by randomly linking lattice sites with linklengths following an exponential distribution with a characteristic scale ζ. We find that this simple spatial network topology does not fulfill any single universality class, but exhibits a new multiuniversality with two sets of critical exponents. This bi-universality is characterized by random–like scaling laws for measurements on a scale smaller than ζ but spatial scaling for measurements on a larger scale. We further explore this topology by studying the resilience of a two-layer multiplex under localized attack. We find that for a broad range of the control parameters, our system is metastable. In this metastable region, a localized attack larger than a critical size — that does not depends on the size of the system — induces a propagating cascade of failures leading to the system collapse.