  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.
