In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically, we propose
a general statistical model to describe network structure. In this model, group is viewed as hidden or unobserved quantity and it is learned by fitting the observed network data using the expectation-maximization algorithm. Compared with existing models, the most prominent strength of our model is the high flexibility. This strength enables it to possess the advantages of existing models and overcomes their shortcomings in a unified way. As a result, not only broad types of structure can be detected without prior knowledge of what type of intrinsic regularities exist in the network, but also the type of identified structure can be directly learned from data. Moreover, by differentiating outgoing edges from incoming edges, our model can detect several types of structural regularities beyond competing models. Tests on a number of real world and artificial networks demonstrate that our model outperforms the state-of-the-art model at shedding light on the structural features of networks, including the overlapping community structure, multipartite structure and several other types of structure which are beyond the capability of existing models.
It has been shown that the communities of complex networks often overlap with each other. However, there is no effective method to quantify the overlapping community structure. In this paper, we propose a metric to address this problem. Instead of as
suming that one node can only belong to one community, our metric assumes that a maximal clique only belongs to one community. In this way, the overlaps between communities are allowed. To identify the overlapping community structure, we construct a maximal clique network from the original network, and prove that the optimization of our metric on the original network is equivalent to the optimization of Newmans modularity on the maximal clique network. Thus the overlapping community structure can be identified through partitioning the maximal clique network using any modularity optimization method. The effectiveness of our metric is demonstrated by extensive tests on both the artificial networks and the real world networks with known community structure. The application to the word association network also reproduces excellent results.
