A fuzzy cluster-validity index based on the topology structure and node attribute in complex networks

Abstract

In community detection problems, a noticeable problem is to defining the number of communities determined by experts or validity indices, most of which determine the shortest or longest distance between clusters’ centers or objects. However, they may not come up with good outcomes especially when the centers of clusters are close together. Most available validity index methods principally concentrate on only one aspect of the graph, topological structure or heterogeneous properties of the vertex and ignore the other. In the majority of real social networks, different clusters share nodes, resulting in the formation of overlapping communities. Thus, the proposed validity index, on the basis of structural and attribute similarity, serves as a fuzzy validity index addressing the overlapping communities, and considering communities in a way that each community has a densely connected sub-graph with homogeneous attribute values. The suggested index calculates the compactness and separation between communities. The compactness criterion, which demonstrates the level of coherence and homogeneity in each community, is calculated by intra and inter-cluster density, and attributes entropy between nodes in a community. The separation criterion is calculated by the distance between communities. A desired community is one with a smaller level of compactness and a larger level of separation. Applying the suggested validity index on data sets shows the superior performance compared to the previous indices.