An Entropic Edge Assortativity Measure

Assortativity or assortative mixing is the tendency of a network’s vertices to connect to others with similar characteristics, and has been shown to play a vital role in the structural properties of complex networks. Most of the existing assortativity measures have been developed on the basis of vertex degree information. However, there is a significant amount of additional information residing in the edges in a network, such as the edge directionality and weights. Moreover, the von Neumann entropy has proved to be an efficient entropic complexity level characterization of the structural and functional properties of both undirected and directed networks. Hence, in this paper we aim to combine these two methods and propose a novel edge assortativity measure which quantifies the entropic preference of edges to form connections between similar vertices in undirected and directed graphs. We apply our novel assortativity characterization to both artificial random graphs and real-world networks. The experimental results demonstrate that our measure is effective in characterizing the structural complexity of networks and classifying networks that belong to different complexity classes.