Silhouette for the evaluation of community structures in multiplex networks

This paper focuses on the silhouette as validity criterion for community structures in networks, with emphasis on multiplex networks. We propose a versatile definition of the silhouette, by generalizing it to encompass different scenarios of proximity between entities in a network, where the distance notion can be geodesic-based or homophily-oriented. To the best of our knowledge, we are the first to propose this twofold perspective on the silhouette and its extension to deal with multiplex networks. We also define an approximate variant of the multiplex silhouette to speed up its computation on large networks, based on the exploitation of central nodes to be regarded as community representatives. Experimental results performed on benchmark real-world network datasets have revealed that the proposed multiplex silhouette is positively correlated with its approximate version, while the latter proved to be much faster in terms of execution time.