Finding optimal assortativity configurations in directed networks

The modelling of many complex systems is usually approached by directed networks where nodes and connections represent the elements of the system and their interactions respectively. The degree-assortativity, which is the tendency of nodes to link to nodes of similar degree, has four components in the digraphs case. In comparison with the undirected graph case, the degree-assortativity of digraphs has not been well studied despite the potential effects that it has to constraint or influence the structural and dynamical properties of a network. Thus, we have considered a random directed network and numerically trained the assortativity profiles of the four components (in-out; out-in; in-in; out-out) by applying degree-preserving rewiring, but we interestingly found that the widely used two-swap method is severely limited. In consequence, we used a much powerful and rather forgotten three-swap method capable to achieve all different assortativities configurations of the given initial random graphs. Secondly, we characterized the obtained networks in relation to other common structural properties such as path length and algebraic connectivity. Finally, by simulating and analysing a dynamical process on the network, we have found that certain profiles cause the network to exhibit enhanced sensitivity to small perturbations without losing their stability.