Behavior and Sublinear Algorithm for Opinion Disagreement on Noisy Social Networks

2026-04-02

AI Summary

This study addresses the challenge of efficiently estimating opinion disagreement under noise perturbations in large-scale sparse scale-free social networks, where existing methods struggle to achieve both accuracy and scalability. Building upon the discrete-time DeGroot model, this work reveals that scale-free network topologies exhibit noise-resilient stability: under white noise perturbations, the level of opinion disagreement converges to a stable constant. To exploit this property, the authors propose the first sublinear-time estimation algorithm with rigorous theoretical error guarantees, integrating truncated random walks with subset sampling to dramatically enhance computational efficiency while preserving high accuracy. Empirical evaluations demonstrate the algorithm’s scalability and practicality on large real-world networks.

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.

Problem

• opinion disagreement
• noisy social networks
• scale-free networks
• sublinear algorithm
• DeGroot model

Innovation

• sublinear algorithm
• opinion disagreement
• scale-free networks
• noisy opinion dynamics
• truncated random walks