Behavior and Sublinear Algorithm for Opinion Disagreement on Noisy Social Networks

TL;DR

This paper investigates how scale-free social network structures influence opinion disagreement under noisy dynamics and introduces a scalable sublinear algorithm for estimating disagreement efficiently.

Contribution

It reveals the resistance of scale-free networks to noise in opinion dynamics and proposes a novel sublinear algorithm for large-scale disagreement estimation.

Findings

Scale-free networks are resistant to noise in opinion disagreement.

The proposed algorithm achieves efficient and accurate estimation of disagreement.

Experiments confirm the scalability and effectiveness of the method.

Abstract

The phenomenon of opinion disagreement has been empirically observed and reported in the literature, which is affected by various factors, such as the structure of social networks. An important discovery in network science is that most real-life networks, including social networks, are scale-free and sparse. In this paper, we study noisy opinion dynamics in sparse scale-free social networks to uncover the influence of power-law topology on opinion disagreement. We adopt the popular discrete-time DeGroot model for opinion dynamics in a graph, where nodes' opinions are subject to white noise. We first study opinion disagreement in many realistic and model networks with a scale-free topology, which approaches a constant, indicating that a scale-free structure is resistant to noise in the opinion dynamics. Moreover, existing algorithms for estimating opinion disagreement are computationally impractical for large-scale networks due to their high computational complexity. To solve this challenge, we introduce a sublinear-time algorithm to approximate this quantity with a theoretically guaranteed error. This algorithm efficiently simulates truncated random walks starting from a subset of nodes while preserving accurate estimation. Extensive experiments demonstrate its efficiency, accuracy, and scalability.