Constructing and sampling graphs with a prescribed joint degree distribution
Journal of Experimental Algorithmics (JEA)
Breaking the speed and scalability barriers for graph exploration on distributed-memory machines
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Inexact subgraph isomorphism in MapReduce
Journal of Parallel and Distributed Computing
Learning mixed kronecker product graph models with simulated method of moments
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Maintaining connected components for infinite graph streams
Proceedings of the 2nd International Workshop on Big Data, Streams and Heterogeneous Source Mining: Algorithms, Systems, Programming Models and Applications
Analyzing future communities in growing citation networks
Proceedings of the 2013 international workshop on Mining unstructured big data using natural language processing
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Graph analysis is playing an increasingly important role in science and industry. Due to numerous limitations in sharing real-world graphs, models for generating massive graphs are critical for developing better algorithms. In this paper, we analyze the stochastic Kronecker graph model (SKG), which is the foundation of the Graph500 supercomputer benchmark due to its many favorable properties and easy parallelization. Our goal is to provide a deeper understanding of the parameters and properties of this model so that its functionality as a benchmark is increased. We develop a rigorous mathematical analysis that shows this model cannot generate a power-law distribution or even a lognormal distribution. However, we formalize an enhanced version of the SKG model that uses random noise for smoothing. We prove both in theory and in practice that this enhancement leads to a lognormal distribution. Additionally, we provide a precise analysis of isolated vertices, showing that graphs that are produced by SKG might be quite different than intended. For example, between 50% and 75% of the vertices in the Graph500 benchmarks will be isolated. Finally, we show that this model tends to produce extremely small core numbers (compared to most social networks and other real graphs) for common parameter choices.