Analytic Treatment of Tipping Points for Social Consensus in Large Random Networks

TL;DR

This paper develops a mathematical model to analyze how social consensus emerges in large random networks, revealing how network connectivity influences the tipping points for consensus and the impact of committed nodes.

Contribution

It introduces a homogeneous pair approximation with a six-dimensional ODE for the Naming Game, providing new insights into the dynamics and tipping points in uncorrelated networks.

Findings

The model accurately predicts the change in dynamical behavior with average degree <k>.

Presence of committed nodes shifts the tipping point in sparse networks.

Results align well with numerical simulations.

Abstract

We introduce a homogeneous pair approximation to the Naming Game (NG) model by deriving a six-dimensional ODE for the two-word Naming Game. Our ODE reveals the change in dynamical behavior of the Naming Game as a function of the average degree < k > of an uncorrelated network. This result is in good agreement with the numerical results. We also analyze the extended NG model that allows for presence of committed nodes and show that there is a shift of the tipping point for social consensus in sparse networks.