Critical behavior of cascading failures in overloaded networks

TL;DR

This paper investigates the critical behavior and universality class of cascading failures in overloaded spatial networks, revealing different transition types depending on link length and similarities to interdependent networks.

Contribution

It identifies the critical exponents and universality class of overload-induced cascades, linking spatial network behavior to interdependent network phase transitions.

Findings

Weakly embedded systems show mixed-order transitions with critical plateaus.

Strongly embedded systems exhibit pure first-order transitions with nucleation.

Critical behavior in both regimes resembles that of interdependent networks.

Abstract

While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered by failures of links and overloads in networks with a spatial characteristic link length $\zeta$. Our results indicate that this abrupt transition has features and critical exponents similar to those of interdependent networks, suggesting that both systems are in the same universality class. For weakly embedded systems (i.e., $\zeta$ of the order of the system size $L$) we observe a mixed-order transition, where the order parameter collapses following a long critical plateau. On the other hand, strongly embedded systems (i.e., $\zeta \ll L$) exhibit a pure first-order transition, involving nucleation and the growth of damage. The system's critical behavior in both limits is similar to that observed in interdependent networks.