Optimal community structure for social contagions

TL;DR

This paper introduces a reversible social contagion model incorporating social reinforcement and community structure, revealing a first-order phase transition, hysteresis effects, and an optimal community configuration for maximizing spread.

Contribution

It presents a novel social contagion model with social reinforcement and community effects, analyzing phase transitions and identifying an optimal community structure for spreading.

Findings

First-order phase transition in spreading dynamics

Hysteresis loop in adoption process

Existence of an optimal community structure

Abstract

Community structure is an important factor in the behavior of real-world networks because it strongly affects the stability and thus the phase transition order of the spreading dynamics. We here propose a reversible social contagion model of community networks that includes the factor of social reinforcement. In our model an individual adopts a social contagion when the number of received units of information exceeds its adoption threshold. We use mean-field approximation to describe our proposed model, and the results agree with numerical simulations. The numerical simulations and theoretical analyses both indicate that there is a first-order phase transition in the spreading dynamics, and that a hysteresis loop emerges in the system when there is a variety of initially-adopted seeds. We find an optimal community structure that maximizes spreading dynamics. We also find a rich phase diagram with a triple point that separates the no-diffusion phase from the two diffusion phases.