Discovering <tex>$k$</tex>-Trusses in Large-Scale Networks

Abstract

A k-truss is a subgraph where every edge belongs to at least k-2 triangles in the subgraph. The truss decomposition assigns each edge the maximum k for which the edge belongs to a k-truss, and the trussness of a graph is the maximum among its edges. Discovery algorithms for k-trusses and truss decomposition provide useful insight for graph analytics (such as community detection). Even though they take polynomial time, on massive networks they suffer from handling a potentially cubic number of wedges: algorithms either need a long time to recompute triangles several times, have high memory usage, or rely on the large number of cores on graphic units. In this paper we describe EXTRUSS, a highly optimized algorithm for truss decomposition which outperforms existing algorithms. We then introduce a faster algorithm, HYBTRUSS, which finds the trussness of a graph using less time and space than EXTRUSS. Our algorithms take the best of existing approaches having good performance, low memory usage, and no need for sophisticated hardware systems. We compare our algorithms with the state-of-the-art on a set of real-world and synthetic networks. EXTRUSS processes graphs with over a billion edges, which seems difficult for the competitors, and our HYBTRUSS is the first algorithm able to find the trussness of a graph with over 25 billion edges.