article

Counting triangles in real-world networks using projections

Author:

Charalampos E. TsourakakisAuthors Info & Claims

Knowledge and Information Systems, Volume 26, Issue 3

Pages 501 - 520

Published: 01 March 2011 Publication History

Abstract

Triangle counting is an important problem in graph mining. Two frequently used metrics in complex network analysis that require the count of triangles are the clustering coefficients and the transitivity ratio of the graph. Triangles have been used successfully in several real-world applications, such as detection of spamming activity, uncovering the hidden thematic structure of the web and link recommendation in online social networks. Furthermore, the count of triangles is a frequently used network statistic in exponential random graph models. However, counting the number of triangles in a graph is computationally expensive. In this paper, we propose the EigenTriangle and EigenTriangleLocal algorithms to estimate the number of triangles in a graph. The efficiency of our algorithms is based on the special spectral properties of real-world networks, which allow us to approximate accurately the number of triangles. We verify the efficacy of our method experimentally in almost 160 experiments using several Web Graphs, social, co-authorship, information, and Internet networks where we obtain significant speedups with respect to a straightforward triangle counting algorithm. Furthermore, we propose an algorithm based on Fast SVD which allows us to apply the core idea of the EigenTriangle algorithm on graphs which do not fit in the main memory. The main idea is a simple node-sampling process according to which node i is selected with probability $${\frac{d_i}{2m}}$$ where di is the degree of node i and m is the total number of edges in the graph. Our theoretical contributions also include a theorem that gives a closed formula for the number of triangles in Kronecker graphs, a model of networks which mimics several properties of real-world networks.

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Cited By

Shun J(2017)ReferencesShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018804Online publication date: 9-Jun-2017
https://dl.acm.org/doi/10.1145/3018787.3018804
Shun J(2017)Conclusion and Future WorkShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018803Online publication date: 9-Jun-2017
https://dl.acm.org/doi/10.1145/3018787.3018803
Shun J(2017)Parallel Wavelet Tree ConstructionShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018802Online publication date: 9-Jun-2017
https://dl.acm.org/doi/10.1145/3018787.3018802
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Counting triangles in real-world networks using projections
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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cover image Knowledge and Information Systems

Knowledge and Information Systems Volume 26, Issue 3

March 2011

169 pages

ISSN:0219-1377

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Copyright © Copyright © 2011 Springer-Verlag London Limited.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 March 2011

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Cited By

Shun J(2017)ReferencesShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018804Online publication date: 9-Jun-2017
https://dl.acm.org/doi/10.1145/3018787.3018804
Shun J(2017)Conclusion and Future WorkShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018803Online publication date: 9-Jun-2017
https://dl.acm.org/doi/10.1145/3018787.3018803
Shun J(2017)Parallel Wavelet Tree ConstructionShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018802Online publication date: 9-Jun-2017
https://dl.acm.org/doi/10.1145/3018787.3018802
Shun J(2017)Parallel Lempel-Ziv FactorizationShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018801Online publication date: 9-Jun-2017
https://dl.acm.org/doi/10.1145/3018787.3018801
Shun J(2017)Parallel Computation of Longest Common PrefixesShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018800Online publication date: 9-Jun-2017
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Shun J(2017)Parallel Cartesian Tree and Suffix Tree ConstructionShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018799Online publication date: 9-Jun-2017
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Shun J(2017)Parallel and Cache-Oblivious Triangle ComputationsShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018798Online publication date: 9-Jun-2017
https://dl.acm.org/doi/10.1145/3018787.3018798
Shun J(2017)Linear-Work Parallel Graph ConnectivityShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018797Online publication date: 9-Jun-2017
https://dl.acm.org/doi/10.1145/3018787.3018797
Shun J(2017)Ligra+: Adding Compression to LigraShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018796Online publication date: 9-Jun-2017
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Shun J(2017)Ligra: A Lightweight Graph Processing Framework for Shared MemoryShared-Memory Parallelism Can Be Simple, Fast, and Scalable10.1145/3018787.3018795Online publication date: 9-Jun-2017
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