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 hea...Show MoreMetadata
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.
Published in: 2008 Eighth IEEE International Conference on Data Mining
Date of Conference: 15-19 December 2008
Date Added to IEEE Xplore: 10 February 2009
Print ISBN:978-0-7695-3502-9
ISSN Information:
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Real Networks ,
- Large Real Networks ,
- Social Networks ,
- Power-law ,
- Excellent Accuracy ,
- Large Graphs ,
- Parallelization ,
- Time Complexity ,
- Undirected ,
- Least-squares Fitting ,
- Matrix Multiplication ,
- Eigenvalues Of Matrix ,
- Degree Distribution ,
- Space Complexity ,
- Eigenvalue Problem ,
- Real-world Networks ,
- Large Computation ,
- High-degree Nodes ,
- Chebyshev Polynomials ,
- Number Of Eigenvalues ,
- Tolerance Parameter ,
- Eigensolver ,
- Forward Algorithm
- Author Keywords
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Real Networks ,
- Large Real Networks ,
- Social Networks ,
- Power-law ,
- Excellent Accuracy ,
- Large Graphs ,
- Parallelization ,
- Time Complexity ,
- Undirected ,
- Least-squares Fitting ,
- Matrix Multiplication ,
- Eigenvalues Of Matrix ,
- Degree Distribution ,
- Space Complexity ,
- Eigenvalue Problem ,
- Real-world Networks ,
- Large Computation ,
- High-degree Nodes ,
- Chebyshev Polynomials ,
- Number Of Eigenvalues ,
- Tolerance Parameter ,
- Eigensolver ,
- Forward Algorithm
- Author Keywords