Higher-order assortativity for directed weighted networks and Markov chains

In this paper, we propose a new class of assortativity measures for weighted and directed networks. We extend Newman's classical degree-degree assortativity by considering node attributes other than degree, and we propose connections among nodes via directed walks of length greater than one, thus obtaining higher-order assortativity. We test the new measure in the paradigmatic case of the world trade network and for other networks from a socioeconomic context, and we also provide some simulation results. Importantly, we show how this global network indicator is strongly related to the autocorrelations of the states of a Markov chain.