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