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In this work, we investigate a heterogeneous population in the modifiedHegselmann-Krause opinion model on complex networks. We introduce the Shannoninformation entropy about all relative opinion clusters to characterize thecluster profile in the final configuration. Independent of network structures,there exists the optimal stubbornness of one subpopulation for the largestnumber of clusters and the highest entropy. Besides, there is the optimalbounded confidence (or subpopulation ratio) of one subpopulation for thesmallest number of clusters and the lowest entropy. However, network structuresaffect cluster profiles indeed. A large average degree favors consensus formaking different networks more similar with complete graphs. The network sizehas limited impact on cluster profiles of heterogeneous populations onscale-free networks but has significant effects upon those on small-worldnetworks.

Clusters and the entropy in opinion dynamics on complex networks