Opinion Dynamics Incorporating Higher-Order Interactions

TL;DR

This paper introduces a novel opinion dynamics model that incorporates higher-order interactions in social networks, providing a more realistic representation of opinion formation and proposing an efficient algorithm for equilibrium estimation.

Contribution

The paper develops a new opinion dynamics model with higher-order interactions and proposes a scalable algorithm for approximating equilibrium opinions.

Findings

Model converges to a fixed opinion vector influenced by higher-order interactions.

Proposed algorithm approximates equilibrium nearly linearly in space and time.

Experiments show the algorithm is both efficient and effective on social networks.

Abstract

The issue of opinion sharing and formation has received considerable attention in the academic literature, and a few models have been proposed to study this problem. However, existing models are limited to the interactions among nearest neighbors, ignoring those second, third, and higher-order neighbors, despite the fact that higher-order interactions occur frequently in real social networks. In this paper, we develop a new model for opinion dynamics by incorporating long-range interactions based on higher-order random walks. We prove that the model converges to a fixed opinion vector, which may differ greatly from those models without higher-order interactions. Since direct computation of the equilibrium opinion is computationally expensive, which involves the operations of huge-scale matrix multiplication and inversion, we design a theoretically convergence-guaranteed estimation algorithm that approximates the equilibrium opinion vector nearly linearly in both space and time with respect to the number of edges in the graph. We conduct extensive experiments on various social networks, demonstrating that the new algorithm is both highly efficient and effective.