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.
单洲君, 彭诗雨, 陈曦. 稳态观点在网络上的分布与聚集研究[J]. 复杂系统与复杂性科学, 2026, 23(4): 27-34.
SHAN Zhoujun, PENG Shiyu, CHEN Xi. Steady-state Opinion: Distribution and Clustering on Networks[J]. Complex Systems and Complexity Science, 2026, 23(4): 27-34.
[1] Axelrod R. The dissemination of culture: a model with local convergence and global polarization[J]. The Journal of Conflict Resolution, 1997, 41(2): 203-226. [2] Weisbuch G, Deffuant G, Amblard F, et al. Meet, discuss, and segregate！[J]. Complexity, 2002, 7(3): 55-63. [3] Weisbuch G. Bounded confidence and social networks[J]. The European Physical Journal B-Condensed Matter, 2004, 38(2): 339-343. [4] Hegselmann R. Opinion dynamics and bounded confidence models, analysis, and simulation[J]. Journal of Artificial Societies and Social Simulation, 2003, 5(3): 2. [5] Deffuant G. Comparing extremism propagation patterns in continuous opinion models[J]. Journal of Artificial Societies and Social Simulation, 2006, 9(3): 8. [6] Zollman K J S. Social network structure and the achievement of consensus[J]. Politics, Philosophy & Economics, 2012, 11(1): 26-44. [7] Kurmyshev E, Juárez H A, González-silva R A. Dynamics of bounded confidence opinion in heterogeneous social networks: Concord against partial antagonism[J]. Physica A: Statistical Mechanics and its Applications, 2011, 390(16): 2945-2955. [8] Jalili M. Social power and opinion formation in complex networks[J]. Physica A: Statistical Mechanics and its Applications, 2013, 392(4): 959-966. [9] Kozma B, Barrat A. Consensus formation on adaptive networks[J]. Physical Review E, 2008, 77(1): 016102. [10] Huang J, Jin X. Opinion formation on evolving and adaptive networks[J]. Journal of Statistical Mechanics: Theory and Experiment, 2019(1): 013202. [11] Herrera J L, Cosenza M G, Tucci K, et al. General coevolution of topology and dynamics in networks[J]. Europhysics Letters, 2011, 95(5): 58006. [12] Hickok A, Kureh Y, Brooks H Z, et al. A bounded-confidence model of opinion dynamics on hypergraphs[J]. SIAM Journal on Applied Dynamical Systems, 2022, 21(1): 1-32. [13] Meng X F, Van Gorder R A, Porter M A. Opinion formation and distribution in a bounded-confidence model on various networks[J]. Physical Review E, 2018, 97(2): 022312. [14] Ben-naim E, Krapivsky P L, Redner S. Bifurcations and patterns in compromise processes[J]. Physica D: Nonlinear Phenomena, 2003, 183(3): 190-204. [15] Fortunato S, Latora V, Pluchino A, et al. Vector opinion dynamics in a bounded confidence consensus model[J]. International Journal of Modern Physics C, 2005, 16(10): 1535-1551. [16] Fennell S C, Burke K, Quayle M, et al. Generalized mean-field approximation for the Deffuant opinion dynamics model on networks[J]. Physical Review E, 2021, 103(1): 012314. [17] Dubovskaya A, Fennell S C, Burke K, et al. Analysis of mean-field approximation for Deffuant opinion dynamics on networks[J]. SIAM Journal on Applied Mathematics, 2023, 83(2): 436-459. [18] 李纲,陈璟浩.突发公共事件网络舆情研究综述[J].图书情报知识,2014(2):111-119. [19] Park J, Barabási A L. Distribution of node characteristics in complex networks[J]. Proceedings of the National Academy of Sciences, 2007, 104(46): 17916-17920. [20] Galas D J, Nykter M, Carter G W, et al. Biological information as set-based complexity[J]. IEEE Transactions on Information Theory, 2010, 56(2): 667-677. [21] Park J, Newman M E J. Origin of degree correlations in the Internet and other networks[J]. Physical Review E, 2003, 68(2): 026112. [22] Pósfai M, Barabási A L. Network Science[M]. Cambridge, UK: Cambridge University Press, 2016. [23] Yu X, Liang Y, Wang X, et al. The network asymmetry caused by the degree correlation and its effect on the bimodality in control[J]. Physica A: Statistical Mechanics and Its Applications, 2021, 572: 125868. [24] Vázquez A, Weigt M. Computational complexity arising from degree correlations in networks[J]. Physical Review E, 2003, 67(2): 027101. [25] Liu S L, Pang S P. Effect of degree correlation on edge controllability of real networks[J]. Chinese Physics B, 2020, 29(10): 100202. [26] Lekivetz R, Sitter R, Bingham D, et al. On algorithms for obtaining orthogonal and near-orthogonal arrays for main-effects screening[J]. Journal of Quality Technology, 2015, 47(1): 2-13.
