Role of hubs in the synergistic spread of behavior.

The spread of behavior in a society has two major features: the synergy of multiple spreaders and the dominance of hubs. While strong synergy is known to induce mixed-order transitions (MOTs) at percolation, the effects of hubs on the phenomena are yet to be clarified. By analytically solving the generalized epidemic process on random scale-free networks with the power-law degree distribution p_{k}∼k^{-α}, we clarify how the dominance of hubs in social networks affects the conditions for MOTs. Our results show that, for α<4, an abundance of hubs drive MOTs, even if a synergistic spreading event requires an arbitrarily large number of adjacent spreaders. In particular, for 2<α<3, we find that a global cascade is possible even when only synergistic spreading events are allowed. These transition properties are substantially different from those of cooperative contagions, which are another class of synergistic cascading processes exhibiting MOTs.

Universality classes of the generalized epidemic process on random networks.

We present a self-contained discussion of the universality classes of the generalized epidemic process (GEP) on Poisson random networks, which is a simple model of social contagions with cooperative effects. These effects lead to rich phase transitional behaviors that include continuous and discontinuous transitions with tricriticality in between. With the help of a comprehensive finite-size scaling theory, we numerically confirm static and dynamic scaling behaviors of the GEP near continuous phase transitions and at tricriticality, which verifies the field-theoretical results of previous studies. We also propose a proper criterion for the discontinuous transition line, which is shown to coincide with the bond percolation threshold.

Generalized epidemic process on modular networks.

Social reinforcement and modular structure are two salient features observed in the spreading of behavior through social contacts. In order to investigate the interplay between these two features, we study the generalized epidemic process on modular networks with equal-sized finite communities and adjustable modularity. Using the analytical approach originally applied to clique-based random networks, we show that the system exhibits a bond-percolation type continuous phase transition for weak social reinforcement, whereas a discontinuous phase transition occurs for sufficiently strong social reinforcement. Our findings are numerically verified using the finite-size scaling analysis and the crossings of the bimodality coefficient.