DOULION: counting triangles in massive graphs with a coin
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Clustering coefficient queries on massive dynamic social networks
WAIM'10 Proceedings of the 11th international conference on Web-age information management
A spectral algorithm for computing social balance
WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
A space efficient streaming algorithm for triangle counting using the birthday paradox
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
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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, SparcifyingEigenTriangle, relies on the spectral properties of power-law networks and the Achlioptas-McSherry sparsification process. SparcifyingEigenTriangle 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.