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.