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This paper proposes a new class of assortativity measures for weighted anddirected networks. We extend the classical Newman's degree-degree assortativityby considering nodes' attributes different from the degree. Moreover, wepropose connections among the nodes through directed paths of length greaterthan one, thus obtaining higher-order assortativity. We provide an empiricalapplication of these measures for the paradigmatic case of the trade network.Importantly, we show how this global network indicator is strongly related tothe autocorrelations of the states of a Markov chain.

Higher order assortativity for directed weighted networks and Markov chains