Construction of simple graphs with a target joint degree matrix and beyond

Abstract

In networking research, it is often desirable to generate synthetic graphs with certain properties. In this paper, we present a new algorithm, 2K_Simple, for exact construction of simple graphs with a target joint degree matrix (JDM). We prove that the algorithm constructs exactly the target JDM and that its running time is linear in the number of edges. Furthermore, we show that the algorithm poses less constraints on the graph structure than previous state-of-the-art construction algorithms. We exploit this flexibility to extend 2K_Simple and design two algorithms that achieve additional network properties on top of the exact target JDM. In particular, 2K_Simple_Clustering produces simple graphs with a target JDM and average clustering coefficient close to a target, while 2K_Simple_Attributes produces exactly simple graphs with a target JDM and joint occurrence of node attribute pairs. We exhaustively evaluate our algorithms through simulation for small graphs, and we also demonstrate their benefits in generating graphs that resemble real-world social networks in terms of accuracy and speed; we reduce the running time by orders of magnitudes compared to previous approaches that rely on Monte Carlo Markov Chains.