Role of hubs in the synergistic spread of behavior
Yongjoo Baek, Kihong Chung, Meesoon Ha, Hawoong Jeong, Daniel Kim

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 , we clarify how the dominance of hubs in social networks affects the conditions for MOTs. Our results show that, for , an abundance of hubs drive MOTs, even if a synergistic spreading event requires an arbitrarily large number of adjacent spreaders. In particular, for , 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…
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