Dynamic modular networks model mediated by confinement

Abstract

We present a model for network transformation mediated by confinement, as a demonstration of a simple network dynamics that has a direct connection with real world quantities. The model has the capacity of generating complex structures similar to real world networks by the use of two parameters. Starting from an Erdös-Rényi network, nodes are randomly selected to be temporarily confined. Confined nodes form new links among themselves at the same pace they lose connections with the outside nodes. As the network evolves according to the parameters of the model, a series of non trivial network characteristics emerge: the formation of stable heterogeneous degree distributions similar to those of empirical networks, an increasing clustering coefficient, and the emergence of communities outside the confined space. Different from the traditional benchmarks used to create modular networks, there is no arbitrary definition of the number of modules, nor node meta-data defining it as a member of a particular community, nor a tunable parameter directly related with expected modularity. Modules emerge as a result of the dynamics while nodes move among them as connections are rewired. The proposed algorithm has the potential to simulate community dynamics cases in situations where time stamped network data is scarce or absent.