Modeling Network Structure using Kronecker Multiplication∗

Given a large, real graph, how can we generate a synthetic graph that matches its properties, i.e., it has similar degree distribution, similar (small) diameter, similar spectrum, etc? We propose to use “Kronecker graphs”, which naturally obey all of the above properties. We present a fast linear time algorithm for fitting the Kronecker graph generation model to real networks. Experiments on large real and synthetic graphs show that Kronecker graphs indeed mimics very well the patterns found in the target graphs. Once fitted, the model parameters and the resulting synthetic graphs can be used for anonymization, extrapolations, and graph summarization.