Are Percolation Transitions always Sharpened by Making Networks Interdependent?

TL;DR

This paper investigates how interdependence affects the nature of percolation transitions, revealing that such transitions can be either discontinuous or continuous depending on network structure, challenging previous assumptions.

Contribution

It demonstrates that interdependent networks do not always exhibit sharper, discontinuous percolation transitions, especially in spatially embedded lattices, providing new insights into network robustness.

Findings

Discontinuous transition in coupled Erdos-Renyi networks.

Continuous transition in fully interdependent diluted lattices.

Transition sharpness varies with network topology.

Abstract

We study a model for coupled networks introduced recently by Buldyrev et al., Nature 464, 1025 (2010), where each node has to be connected to others via two types of links to be viable. Removing a critical fraction of nodes leads to a percolation transition that has been claimed to be more abrupt than that for uncoupled networks. Indeed, it was found to be discontinuous in all cases studied. Using an efficient new algorithm we verify that the transition is discontinuous for coupled Erdos-Renyi networks, but find it to be continuous for fully interdependent diluted lattices. In 2 and 3 dimension, the order parameter exponent $\beta$ is larger than in ordinary percolation, showing that the transition is less sharp, i.e. further from discontinuity, than for isolated networks. Possible consequences for spatially embedded networks are discussed.