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An efficient exact algorithm for triangle listing in large graphs

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Abstract

This paper presents a new efficient exact algorithm for listing triangles in a large graph. While the problem of listing triangles in a graph has been considered before, dealing with large graphs continues to be a challenge. Although previous research has attempted to tackle the challenge, this is the first contribution that addresses this problem on a compressed copy of the input graph. In fact, the proposed solution lists the triangles without decompressing the graph. This yields interesting improvements in both storage requirement of the graphs and their time processing.

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Notes

  1. i.e., we make no difference between (u, v) and (v, u) in \(V\times V\). We also assume that G is simple \(((v,v)\notin E\) for all v, and that there is no multiple edge).

  2. The k-core of a graph is the largest node induced subgraph with a minimum degree of at least k.

  3. http://ferrolab.dmi.unict.it/ri/ri.html#description.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments on earlier drafts of this paper.

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Authors and Affiliations

  1. Université Grenoble Alpes, CNRS, TIMA, LIG, 38000, Grenoble, France

    Sofiane Lagraa

  2. Université de Lyon, CNRS, Université Lyon 1, LIRIS, UMR5205, 69622, Villeurbanne, France

    Hamida Seba

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  1. Sofiane Lagraa
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  2. Hamida Seba
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Correspondence to Hamida Seba.

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Responsible editors: Joao Gama, Indre Zliobaite, Alipio Jorge, and Concha Bielza.

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Lagraa, S., Seba, H. An efficient exact algorithm for triangle listing in large graphs. Data Min Knowl Disc 30, 1350–1369 (2016). https://doi.org/10.1007/s10618-016-0451-4

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