In this work, we investigate a heterogeneous population in the modified Hegselmann–Krause opinion model on complex networks. We introduce the Shannon information entropy about all relative opinion clusters to characterize the cluster profile in the final configuration. Independent of network structures, there exists the optimal stubbornness of one subpopulation for the largest number of clusters and the highest entropy. Besides, there is the optimal bounded confidence (or subpopulation ratio) of one subpopulation for the smallest number of clusters and the lowest entropy. However, network structures affect cluster profiles indeed. A large average degree favors consensus for making different networks more similar with complete graphs. The network size has limited impact on cluster profiles of heterogeneous populations on scale-free networks but has significant effects upon those on small-world networks.

在这项工作中，我们研究了复杂网络上经过修改的Hegselmann-Krause意见模型中的异类种群。我们引入有关所有相对观点聚类的Shannon信息熵，以表征最终配置中的聚类概况。独立于网络结构，对于最大数量的集群和最高的熵，存在一个亚种群的最佳固执。此外，对于最小的聚类数和最低的熵，存在一个子种群的最佳有界置信度（或子种群比率）。但是，网络结构确实会影响群集配置文件。较大的平均程度有助于达成共识，以使不同的网络与完整的图更相似。