Fast Triangle Core Decomposition for Mining Large Graphs

Abstract

Large triangle cores represent dense subgraphs for which each edge has at least k − 2 triangles (same as cliques). This paper presents a fast algorithm for computing the triangle core decomposition on big graphs. The proposed triangle core algorithm adapts both the computations and representation based on the properties of the graph. In addition, we develop a fast edge-based parallel triangle counting algorithm, which lies at the heart of the triangle core decomposition. The proposed algorithm is orders of magnitude faster than the currently available approach. We also investigate and propose fast methods for two variants of the triangle core problem: computing only the top-k triangle cores fast and finding the maximum triangle core number of the graph. The experiments demonstrate the scalability and effectiveness of our approach on 150+ networks with up to 1.8 billion-edges. Further, we apply the proposed methods for graph mining tasks including finding dense subgraphs, temporal strong components, and maximum cliques.