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Enumerating Maximal Clique Sets with Pseudo-Clique Constraint

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Discovery Science (DS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9356))

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Abstract

It is an important task in Data Mining and Social Network Analysis to detect dense subgraphs, namely pseudo-cliques in networks. Given a positive integer k designating an upper bound of the number of disconnections, some algorithms to enumerate k-plexes as pseudo-cliques have been proposed based on the anti-monotonicity property similar to the case of cliques. Those algorithms are however effective only for small k, since every vertex set with its size less than \(k+1\) is trivially a k-plex. Moreover, there still exist non-dense k-plexes with their sizes exceeding k. For these reasons, it has been a hard task to design an efficient k-plex enumerator for non-small k. This paper aims at developing a fast enumerator for finding densely connected k-plexes for non-small k, avoiding both of the small k-plexes and non-dense medium k plexes. For this purpose, we construct a clique-graph from the original input graph and consider meta-cliques of overlapping cliques satisfying several constraints about k-plexness and overlappingness using bond measure for set-theoretic correlation. We also show its usefulness by exhaustive experiments about the number of solution k-plexes, computational costs and even the quality of output k-plexes.

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Notes

  1. 1.

    https://sites.google.com/site/greedycliqueexpansion/.

  2. 2.

    https://github.com/bagrow/linkcomm.

  3. 3.

    http://www.oslom.org/software.htm.

  4. 4.

    http://www.cs.bris.ac.uk/~steve/networks/software/copra.html.

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Authors and Affiliations

  1. Graduate School of Information Science and Technology, Hokkaido University, N-14 W-9, Sapporo, 060-0814, Japan

    Hongjie Zhai, Makoto Haraguchi & Yoshiaki Okubo

  2. The Advanced Algorithms Research Laboratory, The University of Electro-Communications, Chofugoka 1-5-1, Chofu, Tokyo, 182-8585, Japan

    Etsuji Tomita

Authors
  1. Hongjie Zhai
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  2. Makoto Haraguchi
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  3. Yoshiaki Okubo
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  4. Etsuji Tomita
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Corresponding author

Correspondence to Hongjie Zhai .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, Ontario, Canada

    Nathalie Japkowicz

  2. Faculty of Computer Science, Dalhousie University, HALIFAX, Nova Scotia, Canada

    Stan Matwin

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Zhai, H., Haraguchi, M., Okubo, Y., Tomita, E. (2015). Enumerating Maximal Clique Sets with Pseudo-Clique Constraint. In: Japkowicz, N., Matwin, S. (eds) Discovery Science. DS 2015. Lecture Notes in Computer Science(), vol 9356. Springer, Cham. https://doi.org/10.1007/978-3-319-24282-8_28

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  • DOI: https://doi.org/10.1007/978-3-319-24282-8_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24281-1

  • Online ISBN: 978-3-319-24282-8

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