Fast Evaluation for Relevant Quantities of Opinion Dynamics

TL;DR

This paper introduces a nearly linear time algorithm based on Laplacian solvers to efficiently estimate key opinion dynamics metrics in large social networks, overcoming computational challenges of traditional methods.

Contribution

It presents a novel, scalable algorithm that reduces complex matrix operations to vector norm evaluations with theoretical error guarantees.

Findings

Algorithm is efficient and scalable to large networks.

Numerical experiments confirm accuracy and effectiveness.

Method significantly reduces computation time for large graphs.

Abstract

One of the main subjects in the field of social networks is to quantify conflict, disagreement, controversy, and polarization, and some quantitative indicators have been developed to quantify these concepts. However, direct computation of these indicators involves the operations of matrix inversion and multiplication, which make it computationally infeasible for large-scale graphs with millions of nodes. In this paper, by reducing the problem of computing relevant quantities to evaluating $\ell_2$ norms of some vectors, we present a nearly linear time algorithm to estimate all these quantities. Our algorithm is based on the Laplacian solvers, and has a proved theoretical guarantee of error for each quantity. We execute extensive numerical experiments on a variety of real networks, which demonstrate that our approximation algorithm is efficient and effective, scalable to large graphs having millions of nodes.