Title :
Fast Counting of Triangles in Large Real Networks without Counting: Algorithms and Laws
Author :
Tsourakakis, Charalampos E.
Author_Institution :
Machine Learning Dept., Carnegie Mellon Univ., Pittsburgh, PA
Abstract :
How can we quickly find the number of triangles in a large graph, without actually counting them? Triangles are important for real world social networks, lying at the heart of the clustering coefficient and of the transitivity ratio. However, straight-forward and even approximate counting algorithms can be slow, trying to execute or approximate the equivalent of a 3-way database join. In this paper, we provide two algorithms, the eigentriangle for counting the total number of triangles in a graph, and the eigentrianglelocal algorithm that gives the count of triangles that contain a desired node. Additional contributions include the following: (a) We show that both algorithms achieve excellent accuracy, with up to sime 1000x faster execution time, on several, real graphs and (b) we discover two new power laws (degree-triangle and triangleparticipation laws) with surprising properties.
Keywords :
graph theory; security of data; social networking (online); 3-way database; approximate counting algorithms; clustering coefficient; eigentriangle; eigentrianglelocal algorithm; large real networks; real world social networks; transitivity ratio; Application software; Clustering algorithms; Data mining; Eigenvalues and eigenfunctions; Intrusion detection; Machine learning; Machine learning algorithms; Social network services; Web sites; Wikipedia; Graph Generators; Graph Mining; Power laws; Triangles;
Conference_Titel :
Data Mining, 2008. ICDM '08. Eighth IEEE International Conference on
Conference_Location :
Pisa
Print_ISBN :
978-0-7695-3502-9
DOI :
10.1109/ICDM.2008.72
