Patterns of Nonlinear Opinion Formation on Networks

TL;DR

This paper explores how the spectral properties of network adjacency matrices determine whether agents reach consensus or disagreement in nonlinear opinion dynamics, highlighting the role of eigenvector centrality and network symmetry.

Contribution

It provides a spectral characterization of opinion formation patterns in nonlinear network dynamics, linking eigenvalues and eigenvectors to agreement and disagreement outcomes.

Findings

Spectral properties fully characterize opinion outcomes.

Eigenvector centrality influences opinion sensitivity.

Network symmetry impacts opinion cascade patterns.

Abstract

When communicating agents form opinions about a set of possible options, agreement and disagreement are both possible outcomes. Depending on the context, either can be desirable or undesirable. We show that for nonlinear opinion dynamics on networks, and a variety of network structures, the spectral properties of the underlying adjacency matrix fully characterize the occurrence of either agreement or disagreement. We further show how the corresponding eigenvector centrality, as well as any symmetry in the network, informs the resulting patterns of opinion formation and agent sensitivity to input that triggers opinion cascades.