Belief Dynamics in Social Networks: A Fluid-Based Analysis

TL;DR

This paper introduces a fluid-based mathematical framework for modeling and analyzing the evolution of beliefs in social networks, providing insights into steady-state and transient belief dynamics.

Contribution

It develops a general dynamical model of social interactions and derives a diffusion differential equation to analyze belief evolution, including closed-form solutions and semi-analytical methods.

Findings

Closed-form steady-state belief distributions for certain systems

Efficient semi-analytical techniques for general systems

Method applicable to large-scale social networks

Abstract

The advent and proliferation of social media have led to the development of mathematical models describing the evolution of beliefs/opinions in an ecosystem composed of socially interacting users. The goal is to gain insights into collective dominant social beliefs and into the impact of different components of the system, such as users' interactions, while being able to predict users' opinions. Following this thread, in this paper we consider a fairly general dynamical model of social interactions, which captures all the main features exhibited by a social system. For such model, by embracing a mean-field approach, we derive a diffusion differential equation that represents asymptotic belief dynamics, as the number of users grows large. We then analyze the steady-state behavior as well as the time dependent (transient) behavior of the system. In particular, for the steady-state distribution, we obtain simple closed-form expressions for a relevant class of systems, while we propose efficient semi-analytical techniques in the most general cases. At last, we develop an efficient semi-analytical method to analyze the dynamics of the users' belief over time, which can be applied to a remarkably large class of systems.