"Dynamics on Modular Networks with Heterogeneous Correlations"

Another one of my papers came out in final form today. (That's two days in a row, and there is a third that will be out imminently.) Here are the details.

Title: Dynamics on Modular Networks with Heterogeneous Correlations

Authors: Sergey Melnik, Mason A. Porter, Peter J. Mucha, and James P. Gleeson


Abstract: We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module, and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and Lancichinetti-Fortunato-Radicchi networks) by allowing a heterogeneous distribution of degree- degree correlations across modules, which is important for the consideration of nonidentical interactingnetworks.


The basic idea is that we have developed a new random-graph ensemble that allows one to consider heterogeneous levels of homophily (which, in this paper, we use as degree homophily) in different parts of a network. You can also relate this to metapopulations in biology. We examine some simple dynamical processes on such ensembles.