Multiplexity-facilitated cascades in networks

TL;DR

This paper demonstrates that multiplex networks, with multiple interaction types, are more prone to global cascades than single-layer networks, and shows how layer interactions influence cascade dynamics and control.

Contribution

The authors extend the threshold cascade model to multiplex networks, revealing how layer interactions enhance cascade susceptibility and offering new control strategies.

Findings

Multiplex networks are more vulnerable to cascades than simplex networks.

Layer coupling can enable cascades even if individual layers are resistant.

Controlling cascades is possible by modifying the network's layered structure.

Abstract

Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex networks. We generalize the threshold cascade model [D. J. Watts, Proc. Natl. Acad. Sci. U.S.A. 99, 5766 (2002)] to multiplex networks, in which a node activates if a sufficiently large fraction of neighbors in any layer are active. We show that both combining layers (i.e., realizing other interactions play a role) and splitting a network into layers (i.e., recognizing distinct kinds of interactions) facilitate cascades. Notably, layers unsusceptible to global cascades can cooperatively achieve them if coupled. On one hand, this suggests fundamental limitations on predicting cascades without full knowledge of a system's multiplexity; on the other hand, it offers feasible means to control cascades by introducing or removing sparse layers in an existing network.