Spectral Counting of Triangles in Power-Law Networks via Element-Wise Sparsification

• Published in: 2009 International Conference on Advances in Social Network Analysis and Mining : 20-22 July 2009 pp. 66 - 71
• Main Authors: Tsourakakis, C.E., Drineas, P., Michelakis, E., Koutis, I., Faloutsos, C.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.07.2009
• Subjects: Computer science; Density measurement; eigenvalues; Eigenvalues and eigenfunctions; Intrusion detection; Matrix converters; Social network services; social networks; Sparse matrices; Spectral analysis; Statistical analysis; Statistical distributions; triangles
• ISBN: 9780769536897; 0769536891
• DOI: 10.1109/ASONAM.2009.32

Triangle counting is an important problem in graph mining. The clustering coefficient and the transitivity ratio,two commonly used measures effectively quantify the triangle density in order to quantify the fact that friends of friends tend to be friends themselves. Furthermore, several successful graph mining applications rely on the number of triangles. In this paper, we study the problem of counting triangles in large, power-law networks. Our algorithm, SparsifyingEigenTriangle, relies on the spectral properties of power-law networks and the Achlioptas-McSherry sparsification process. SparsifyingEigenTriangle is easy to parallelize, fast and accurate. We verify the validity of our approach with several experiments in real-world graphs, where we achieve at the same time high accuracy and important speedup versus a straight-forward exact counting competitor.