Modularity Based Hierarchical Community Detection in Networks

Abstract

The organization of nodes in communities, i.e., groups of nodes with many internal connections and few external connections, is one of the main structural features of networks and community detection is one of the most challenging tasks in networks. The communities in networks can be observed in different levels and a great number of methods can be found in the literature in order to identify the hierarchical organization of the communities. This work proposes a methodology for the representation of the hierarchical organization of communities in complex networks based on the spectral method of Newman. The proposed methodology, in contrast to other traditional approaches found in the literature, use the modularity, one of the most adopted measures for the quality of communities, in order to define the distances between the communities in the network. The methodology provides, as output, a dendrogram in order to illustrate the hierarchical organization of communities in networks. The application of the methodology to large scale networks show that the hierarchical visualization enhances the understanding of the complex systems modelled by networks, providing a broader view of the community structures.