Triangle listing in massive networks

Abstract

Triangle listing is one of the fundamental algorithmic problems whose solution has numerous applications especially in the analysis of complex networks, such as the computation of clustering coefficients, transitivity, triangular connectivity, trusses, etc. Existing algorithms for triangle listing are mainly in-memory algorithms, whose performance cannot scale with the massive volume of today's fast growing networks. When the input graph cannot fit in main memory, triangle listing requires random disk accesses that can incur prohibitively huge I/O cost. Some streaming, semistreaming, and sampling algorithms have been proposed but these are approximation algorithms. We propose an I/O-efficient algorithm for triangle listing. Our algorithm is exact and avoids random disk access. Our results show that our algorithm is scalable and outperforms the state-of-the-art in-memory and local triangle estimation algorithms.