A similarity-based assortativity measure for complex networks

There are several metrics that have been proposed to quantify the tendency of nodes to link with similar nodes in complex networks. Among them, the assortativity coefficient put forth by M.E.J. Newman has been successfully used in many cases with either categorical or scalar attributes of network nodes. Unfortunately, the assortativity coefficient cannot deal with vectorial attributes. Furthermore, we show that, in certain cases, it may not be able to capture the similarity of neighbors. In this work, we introduce a new metric that, without being much more complex to calculate, solves those problems. Moreover, we show that the proposed metric includes the categorical assortativity coefficient as a particular case. We also study the behavior of the new metric with a few illustrative real-world examples.