Multistage Complex Contagions in Random Multiplex Networks

Yong Zhuang, Osman Yagan

Abstract: Complex contagion models have been developed to understand a wide range of social phenomena, such as adoption of cultural fads, the diffusion of belief, norms, and innovations in social networks, and the rise of collective action to join a riot. Most existing works focus on contagions where individuals' states are represented by binary variables, and propagation takes place over a single isolated network. However, characterization of an individual's standing on a given matter as a binary state might be overly simplistic as most of our opinions, feelings, and perceptions vary over more than two states. Also, most real-world contagions take place over multiple networks (e.g., Twitter and Facebook) or involve multiplex networks where individuals engage in different types of relationships (e.g., acquaintance, coworker, family, etc.). To this end, this paper studies multistage complex contagions that take place over multilayer or multiplex networks. Under a linear threshold based contagion model, we first give analytic results for the expected size of global cascades, that is, cases where a randomly chosen node can initiate a propagation that eventually reaches a positive fraction of the whole population. Next, we analytically derive the probability of triggering global cascades. Then, analytic results are confirmed and supported by an extensive numerical study. In addition, we demonstrate how the dynamics of complex contagions is affected by the extra weight exerted by hyperactive nodes and by the structural properties of the networks. In particular, we reveal an interesting connection between the assortativity of a network and the impact of hyperactive nodes on the cascade size.