Assortative Configuration Random Graphs

Abstract

A random graph model is introduced, which is supposed to capture the assortativity effect in various real-world networks. An effect that appears when different types of vertices have non-uniform tendencies to connect to each other. Therefore, given the node- and edge-type distributions P, Q a discrete matching method is developed, so that the empirical distributions asymptotically passes to their given limits P, Q. Applications of martingale convergence methods are exploited to prove the large n limits of the discrete Markov setup. Finally, the relation between inhomogeneous random graph model as another recently studied topic and our model is investigated.