A scale-free structure for real world networks

Abstract

The field of High Performance Computing (HPC) is defined by application in physics and engineering. These problems drove the development of libraries such as LAPACK, which cast their performance in terms of more specialized building block such as the BLAS. Now that we see a rise in simulation and computational analysis in fields such as biology and the social sciences, how do we leverage existing HPC approaches to these domains. The GraphBLAS project reconciles graph analytics with the machinery of linear algebra libraries. Like their Dense Linear Algebra (DLA) counterpart, the GraphBLAS expresses complex operations in terms of smaller primitives. This paper focuses on efficiently storing real world networks, such that for these graph primitives we can obtain the level of performance seen in DLA. We provide a hierarchical data structured called GERMV, which is an extension of our previous Recursive Matrix Vector (RMV). If the network in question exhibits a scale-free structure, namely hierarchical communities, then our data structure enables high performance. We demonstrate high performance for Sparse Matrix Vector (spMV) and PageRank on real world web graphs.