Similarity matrix average for aggregating multiplex networks

Abstract

We introduce a methodology based on averaging similarity matrices with the aim of integrating the layers of a multiplex network into a single monoplex network. Multiplex networks are adopted for modelling a wide variety of real-world frameworks, such as multi-type relations in social, economic and biological structures. More specifically, multiplex networks are used when relations of different nature (layers) arise between a set of elements from a given population (nodes). A possible approach for analyzing multiplex similarity networks consists in aggregating the different layers in a single network (monoplex) which is a valid representation—in some sense—of all the layers. In order to obtain such an aggregated network, we propose a theoretical approach—along with its practical implementation—which stems on the concept of similarity matrix average. This methodology is finally applied to a multiplex similarity network of statistical journals, where the three considered layers express the similarity of the journals based on co-citations, common authors and common editors, respectively.

Keywords

• multiplex network
• similarity matrix
• Jaccard coefficient
• cosine similarity
• SimRank
• Fréchet mean