Detecting groups of similar components in complex networks

We study how to detect groups in a complex network each of which consists of component nodes sharing a similar connection pattern. Based on the mixture models and the exploratory analysis set up by Newman and Leicht (Newman and Leicht 2007 {\it Proc. Natl. Acad. Sci. USA} {\bf 104} 9564), we develop an algorithm that is applicable to a network with any degree distribution. The partition of a network suggested by this algorithm also applies to its complementary network. In general, groups of similar components are not necessarily identical with the communities in a community network; thus partitioning a network into groups of similar components provides additional information of the network structure. The proposed algorithm can also be used for community detection when the groups and the communities overlap. By introducing a tunable parameter that controls the involved effects of the heterogeneity, we can also investigate conveniently how the group structure can be coupled with the heterogeneity characteristics. In particular, an interesting example shows a group partition can evolve into a community partition in some situations when the involved heterogeneity effects are tuned. The extension of this algorithm to weighted networks is discussed as well.