Complex Social Contagions on Weighted Networks Considering Adoption Threshold Heterogeneity

Jiazhi Ren,Qiwen Yang,Xuzhen Zhu,Hui Tian,Yuxiao Zhu,Wei Wang,Shimin Cai

doi:10.1109/access.2020.2984615

Abstract

Many real-world phenomena can be described as complex contagions, which has attracted much attention in the field of network science. However, the effects of the heterogeneous adoption thresholds on complex contagions in weighted networks have not been systematically investigated. In this paper, we propose a heterogeneous complex contagion model on the weighted network, in which individuals have different adoption thresholds. For individuals with a relatively small adoption threshold, they are more likely to adopt the contagion and act as activists. An edge-weight based compartmental theory is developed to unveil spreading dynamics. Through extensive numerical simulations and theoretical analysis, we find that, for any weight distribution heterogeneity, with the increase of the activist fraction, the growth pattern of the final adoption size versus the information spreading probability changes from hybrid phase transition to a second-order continuous phase transition. Meanwhile, increasing the activist fraction can promote behavior spreading. Through bifurcation analysis, we discover that changing the heterogeneity of the weight distribution will not change the type of phase transition. Besides, reducing weight distribution heterogeneity can facilitate behavior spreading. Extensive numerical simulations verify that the theoretical solutions coincide with the numerical results very well.

Highlights

As an important media for information spreading, social network [1]–[6] facilitate people to transmit information, such as to recommend commodities, to forward news, to exchange information, and so on [7]–[10]
In complex contagion, researchers ignore the heterogeneous adoption effect on weighted social networks with the consideration of social reinforcement derived from the memory of non-redundant information
At first, concerning the heterogeneous adoption, we divide the population into activists and conservatives with a tunable fraction, assign heterogeneous weights to the complex network using weight distribution

Summary

Introduction

As an important media for information spreading, social network [1]–[6] facilitate people to transmit information, such as to recommend commodities, to forward news, to exchange information, and so on [7]–[10]. The edges representing the social interconnection rela-. Social ties may be intimate or distant. Even for the close relation, the strength can be strong or weak. Weighted edges in a weighted network can reasonably model the ties in social networks [17], [18], such as denoting the strength of reputation in scientific network [19], [20], number of calls in communication networks [21], the public cooperation on interdependent networks [22], the number of passengers between two airports in the airline network [23]

Objectives

Methods

Results

Conclusion