Copula-based modeling of degree-correlated networks

Dynamical processes on complex networks such as information exchange, innovation diffusion, cascades in financial networks or epidemic spreading are highly affected by their underlying topologies as characterized by, for instance. degree degree correlations. Here, we introduce the concept of copulas in order to generate random networks with an arbitrary degree distribution and a rich a priori degree degree correlation (or 'association') structure. The accuracy of the proposed formalism and corresponding algorithm is numerically confirmed, While the method is tested on a real-world network of yeast, protein protein interactions. The derived network ensembles can be systematically deployed as proper null models, in order to unfold the complex interplay between the topology of real-world networks and the dynamics on top of them.