A Scalable Generative Graph Model with Community Structure

Tamara G. Kolda, Ali Pinar, Todd D. Plantenga, C. Seshadhri

Abstract: Network data is ubiquitous and growing, yet we lack realistic generative network models that can be calibrated to match real-world data. The recently proposed block two-level Erdös--Rényi (BTER) model can be tuned to capture two fundamental properties: degree distribution and clustering coefficients. The latter is particularly important for reproducing graphs with community structure, such as social networks. In this paper, we compare BTER to other scalable models and show that it gives a better fit to real data. We provide a scalable implementation that requires only $O(d_{\rm max})$ storage, where $d_{\rm max}$ is the maximum number of neighbors for a single node. The generator is trivially parallelizable, and we show results for a Hadoop MapReduce implementation for modeling a real-world Web graph with over 4.6 billion edges. We propose that the BTER model can be used as a graph generator for benchmarking purposes and provide idealized degree distributions and clustering coefficient profiles that can be tuned for user specifications.