Community discovery plays a crucial role in understanding the structure of networks. In recent years, the application of clustering algorithms in the community-discovery tasks of complex networks has been studied frequently. In this study, we proposed a balance factor of node density and node-degree centrality for the core-node selection problem in community discovery. We also proposed a new community-discovery algorithm based on the balance factor, adaptability, and modularity increment, which is based on the balance factor (BComd). First, the proposed method was able to identify the core nodes in a community. Second, we used node-degree centrality, node density, and adaptability to detect overlaps between communities and then we removed these overlaps from the network to obtain a subnetwork with a clear community structure. Third, we obtained the preliminary community divisions by clustering the subnetworks, and these preliminary communities were usually the core parts of the communities they belonged to. Finally, each preliminary community was compressed into a new node, and then, the new network was clustered using the Louvain algorithm. The experimental results showed that the algorithm identified the core nodes in communities well, effectively discovered overlaps between communities, and had superior performance in large-scale networks.
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