Extending assortativity: An application to weighted social networks

Assortativity by degree for complex networks is quantified by the Newman coefficient, and it describes a tendency for nodes to be connected to others with a similar degree. A generalization of the assortativity index has been proposed in the literature for undirected and unweighted networks, analysing the correlation between vertices that are not necessarily adjacent, but connected through paths, shortest paths and random walks. The aim of this study is to define a new class of higher-order assortativity measures for weighted networks. The effectiveness of these measures is evident in social networks, where both weights and connections are significant. Applications to Facebook and co-authorship networks are provided, analysing the assortativity beyond the nearest neighbours.