Generation of scale-free assortative networks via Newman rewiring for simulation of diffusion phenomena

Abstract

By collecting and expanding several numerical recipes developed in previous work, we implement an object-oriented Python code, based on the networkX library, for the realization of the configuration model and Newman rewiring. The software can be applied to any kind of network and "target" correlations, but it is tested with focus on scale-free networks and assortative correlations. For generating the degree sequence we use the method of "random hubs", which gives networks with minimal fluctuations. For the assortative rewiring we use the simple Vazquez-Weigt matrix as a test in the case of random networks; since it appears to be not effective in the case of scale-free networks we then turn to another recipe which generates matrices with decreasing off-diagonal elements. The rewiring procedure is important also at the theoretical level, in order to test which types of statistically acceptable correlations can actually be realized in concrete networks. From the applicative point of view, its main use is in the construction of correlated networks for the solution of dynamical or diffusion processes by analyzing the evolution of single nodes, i.e., beyond the Heterogeneous Mean Field approximation. As an example, we report on an application to the Bass diffusion model, with calculations of the time $t_{max}$ of the diffusion peak. The same networks can additionally be exported in environments for agent-based simulations like NetLogo.