Role of hubs in the synergistic spread of behavior

TL;DR

This paper analytically investigates how hubs in scale-free networks influence the emergence of mixed-order transitions in the spread of behavior, revealing that hubs significantly facilitate global cascades under synergy.

Contribution

It provides a theoretical analysis of the role of hubs in synergistic spreading on scale-free networks, highlighting conditions for mixed-order transitions based on degree distribution.

Findings

Hubs promote mixed-order transitions for degree exponent α<4.

Global cascades can occur with only synergistic spreading for 2<α<3.

Results differ from cooperative contagions in transition behavior.

Abstract

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 $p_k \sim k^{-\alpha}$, we clarify how the dominance of hubs in social networks affects the conditions for MOTs. Our results show that, for $\alpha < 4$, an abundance of hubs drive MOTs, even if a synergistic spreading event requires an arbitrarily large number of adjacent spreaders. In particular, for $2 < \alpha < 3$, 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.