The effect of network structure on bounded confidence opinion dynamics

doi:10.23919/JSEE.2026.000057

Abstract

Abstract:

Resolving conflict and achieving consensus among social groups with diverse opinions becomes a critical issue in today’s extensively connected society. Despite the ubiquitous heterogeneity of connection or contact patterns, the study of how topological characteristics of network structure affect opinion convergence is still insufficient. Based on Deffuant and colleagues’ bounded confidence model and the transformable network structure between random network and typical complex network types, including small-world network and scale-free network, we analyze the critical factors affecting continuous opinion convergence. We find that the network density plays a crucial role in the aggregated process of opinions in the social group, followed by the modularized level and the average shortest path length of the social network. However, the structural features have little impact on the consensus phase transition threshold. The further simulation experiments under real networks can be well understood based on the interplay of these three main factors. These findings confirm the paramount importance of creating a high-frequency and widely communicated atmosphere to mitigate conflict and efficiently reach consensus.

Key words: consensus and divergence, opinion dynamics, bounded confidence model, complex network

Miao DU, Jianfeng CAI. The effect of network structure on bounded confidence opinion dynamics[J]. Journal of Systems Engineering and Electronics, 2026, 37(2): 521-533.

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Network structure	Network density
Scale-free	0.004132
Lattice	0.008282
Small world	0.012003
Well-mixed population	1

Population	Intercept		Slope		Adj. R-Square
Population	Value	Standard Error	Value	Standard Error	Adj. R-Square
100	0.10458	0.05275	0.02089	0.00369	0.5741
200	0.38796	0.02213	0.0338	0.00155	0.95382
500	0.6966	0.02631	0.05281	0.00184	0.97277
1000	0.99413	0.05084	0.08575	0.00356	0.96185

Skewness value	100	200	500	1000
Coefficient (network density)	0.536	0.785	0.844	0.833
Coefficient (lodularity)	−0.111	−0.236	−0.311	−0.334
Coefficient (ASPL)	−0.229	−0.151	−0.044	−0.052
R-squared	0.565	0.972	0.979	0.971
F-statistic	8.642	229.7	308.2	225.4
Prob (F-statistic)	0.000705	1.16e−15	6.64e−17	1.40e−15

Type	Facebook	Collaboration	Email
Nodes	4039	4158	1133
Edges	88234	13428	6555
Network density	0.011	0.00155	0.01
Average clustering coefficient	0.6055	0.557	0.1689
ASPL	3.692	6.049	2.898
Modularity	0.83	0.846	0.477

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