Weighted-spectral clustering algorithm for detecting community structures in complex networks

The community structure is a common non-trivial topological feature of many complex real-world networks. Existing methods for identifying the community structure are generally based on statistical-type properties, such as the degree of centrality, the shortest path betweenness centrality, the modularity, and so forth. However, the form of the community structure may vary widely, even if the number of vertices and edges are fixed. Consequently, it is difficult to be certain of the exact number of clusters within the network. Clustering schemes which require the number of clusters to be specified in advance often misjudge the community structure and yield a poor clustering performance as a result. Accordingly, the present study proposes a clustering algorithm, designated as the Weighted-Spectral Clustering Algorithm, capable of detecting the community structure of a network with no prior knowledge of the cluster number. The proposed method is tested on both computer-generated networks and several real-world networks for which the community structures are already known. The results confirm the ability of the proposed algorithm to partition the network into an appropriate number of clusters in every case.