The Inclusion Measure for Community Evaluation and Detection in Unweighted Networks

One of the most interesting problems in network analysis is community detection, i.e. the partitioning of nodes into communities, with many edges connecting nodes of the same community and comparatively few edges connecting nodes of different communities. We introduce a new quality measure to evaluate a partitioning of an undirected and unweighted graph into communities that is called inclusion. This quality measure evaluates how well each node is included in its community by considering both its existent and its non-existent edges. We have implemented a strategy that maximizes the inclusion criterion by moving each time a single node to another community. We also considered inclusion as a criterion for evaluating partitions provided by spectral clustering. In our experimental study, the inclusion criterion is compared to the widely used modularity criterion providing improved community detection results without requiring the a priori specification of the number of communities.