Source-linked AI summary
Multiplexity-facilitated cascades in networks
Charles D. Brummitt, Kyu-Min Lee, K. -I. Goh
TL;DR
The paper asks how multiple interaction types affect global cascades and generalizes the threshold model to multiplex networks. It finds that combining or splitting layers facilitates cascades, including through cooperation between individually non-cascading layers, with implications for cascade control.
Problem
Single-edge network models cannot capture non-additive influence across multiple interaction channels, motivating analysis of multiplexity in cascade dynamics.
Method
The authors generalize Watts’ threshold model so a node activates when the active-neighbor fraction in any layer exceeds its threshold, analyzing multiplex networks analytically and numerically.
Results
Both combining layers and splitting networks into layers facilitate global cascades, while layers that cannot cascade alone can achieve cascades cooperatively when multiplex-coupled.
Takeaways & Limitations
Cascade predictions require accounting for network multiplexity, and sparse layers below the percolation threshold can provide a feasible means of controlling cascades.
Takeaways & Limitations
The analysis assumes that all nodes have the same threshold R.
Abstract
from arXiv · showhide
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.