1112.0093 (Charles D. Brummitt et al.)

Multiplexity-facilitated cascades in networks    [PDF]

Charles D. Brummitt, Kyu-Min Lee, K. -I. Goh

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, PNAS
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 adding 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 adding or removing sparse layers to an existing network.

View original: http://arxiv.org/abs/1112.0093