Assortative mixing in weighted directed networks

Abstract

We analyse assortative mixing, the tendency of vertices to bond with others based on similarities (usually excess vertex degree), in weighted networks, both directed and undirected. We propose a generalisation of the concept of assortativity by introducing our generalised assortativity coefficient. We also provide procedures that allow for both precisely assessing and interpreting the assortativity of weighted networks as well as its statistical significance. Finally, we demonstrate the usefulness of our proposed generalised assortativity coefficient by in-depth analysing the assortativity structure of several weighted real-world networks.