Social dynamics with peer support on heterogeneous networks: The "mafia model"

TL;DR

This paper introduces a model of social dynamics on heterogeneous networks, highlighting how peer support influences opinion formation and community states, with a focus on scale-free network structures and external influences.

Contribution

It presents a novel non-linear model incorporating peer support proportional to local neighborhood composition on scale-free networks.

Findings

Coexistence of multiple opinions and consensus states are possible.

Network heterogeneity critically affects social dynamics.

External control elements influence community opinion states.

Abstract

Human behavior often exhibit a scheme in which individuals adopt indifferent, neutral, or radical positions on a given topic. The mechanisms leading to community formation are strongly related with social pressure and the topology of the contact network. Here, we discuss an approach to model social behavior which accounts for the protection by alike peers proportional to their relative abundance in the closest neighborhood. We explore the ensuing non-linear dynamics emphasizing the role of the specific structure of the social network, modeled by scale-free graphs. We find that both coexistence of opinions and consensus on the default position are possible stationary states of the model. In particular, we show how these states critically depend on the heterogeneity of the social network and the specific distribution of external control elements.