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| Steady-state Opinion: Distribution and Clustering on Networks |
| SHAN Zhoujun, PENG Shiyu, CHEN Xi
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| School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China |
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Abstract The paper addresses an overlooked phenomenon in opinion dynamics research: the clustering of identical opinions on network topology. The paper investigates the distribution and clustering of steady-state opinions on networks through the probability distribution function of the proportion of neighbors holding different opinion around a specific type of opinion. Simulations of the Deffuant-Weisbuch model′s opinion diffusion process reveal two key characteristics of steady-state opinion distributions in ER random graphs converging into two opinion clusters: the probability distribution function follows a binomial distribution, and identical opinion aggregation induces a probability bias, where the product of the bias and the network′s average degree remains constant. Building upon these findings, this study extends the results to small-world networks and examines how clustering coefficient influences the steady-state distribution and clustering of opinions, thereby further validating and broadening the general applicability of the research outcomes.
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Published: 15 September 2026
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