Using multiple-criteria methods to evaluate community partitions

Community detection is one of the most studied problems on complex networks. Although hundreds of methods have been proposed so far, there is still no universally accepted formal definition of what is a good community. As a consequence, the problem of the evaluation and the comparison of the quality of the solutions produced by these algorithms is still an open question, despite constant progress on the topic. In this article, we investigate how using a multi-criteria evaluation can solve some of the existing problems of community evaluation, in particular the question of multiple equally-relevant solutions of different granularity. After exploring several approaches, we introduce a new quality function, called MDensity, and propose a method that can be related both to a widely used community detection metric, the Modularity, and to the Precision/Recall approach, ubiquitous in information retrieval