Social Influence in Signed Networks

Social influence has been widely discussed in various disciplines due to its important sociological significance. However, the dynamics of social influence in signed networks have nonetheless received fairly little attention. In this article, we propose a generalized Pólya urn model that considers the effect of negative relationships and is capable of comprehending the specific mechanisms of homophily and xenophobia in the dynamics. Based on the mathematical deduction, we find that the signed network guides social influence in a trend toward equality. Simulation shows that a higher effect or larger proportion of negative relationships may break the self-reinforcement and make the market more equal. The collective dynamics in the signed network are more predictable but generate path dependence. We also find that a balanced structure has no impact on the average market share but is helpful in removing path dependence and promoting system stability.