Intersection Representation of Big Data Networks and Triangle Enumeration

Abstract

AbstractTriangles are an essential part of network analysis, representing metrics such as transitivity and clustering coefficient. Using the correspondence between sparse adjacency matrices and graphs, linear algebraic methods have been developed for triangle counting and enumeration, where the main computational kernel is sparse matrix-matrix multiplication. In this paper, we use an intersection representation of graph data implemented as a sparse matrix, and engineer an algorithm to compute the “k-count” distribution of the triangles of the graph. The main computational task of computing sparse matrix-vector products is carefully crafted by employing compressed vectors as accumulators. Our method avoids redundant work by counting and enumerating each triangle exactly once. We present results from extensive computational experiments on large-scale real-world and synthetic graph instances that demonstrate good scalability of our method. In terms of run-time performance, our algorithm has been found to be orders of magnitude faster than the reference implementations of the miniTri data analytics application [18].KeywordsIntersection matrixLocal triangle countForward degree cumulativeForward neighboursSparse graphk-count