Analysis of complex contagions in random multiplex networks

Details Analysis of complex contagions in random multiplex networks Analysis of complex contagions in random multiplex networks

2012-04-02

arxiv.org/abs/1204.0491v2

Physics

Physics and Society

10 Pages, 2 figures

Scientific paper

We study the diffusion of influence in random multiplex networks where links can be of $r$ different types, and for a given content (e.g., rumor, product, political view), each link type is associated with a content dependent parameter $c_i$ in $[0,\infty]$ that measures the relative bias type-$i$ links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their "perceived" proportion of active neighbors exceeds a threshold \tau. Namely, a node connected to $m_i$ active neighbors and $k_i-m_i$ inactive neighbors via type-$i$ links will turn active if $\sum{c_i m_i}/\sum{c_i k_i}$ exceeds its threshold \tau. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network exhibits an unusual behavior in that a global spreading event may still be possible even if the network does not posses a giant vulnerable cluster. This last finding signals a contradiction with the behavior of the existing models in the literature, and reinforces the need for link classification in complex networks.

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