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Community detection in directed acyclic graphs

The European Physical Journal B volume 88, Article number: 203 (2015) Cite this article

Abstract

Some temporal networks, most notably citation networks, are naturally represented as directed acyclic graphs (DAGs). To detect communities in DAGs, we propose a modularity for DAGs by defining an appropriate null model (i.e., randomized network) respecting the order of nodes. We implement a spectral method to approximately maximize the proposed modularity measure and test the method on citation networks and other DAGs. We find that the attained values of the modularity for DAGs are similar for partitions that we obtain by maximizing the proposed modularity (designed for DAGs), the modularity for undirected networks and that for general directed networks. In other words, if we neglect the order imposed on nodes (and the direction of links) in a given DAG and maximize the conventional modularity measure, the obtained partition is close to the optimal one in the sense of the modularity for DAGs.

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Authors and Affiliations

  1. Department of Mathematical Informatics, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-8656, Japan

    Leo Speidel

  2. JST, ERATO, Kawarabayashi Large Graph Project, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Leo Speidel & Taro Takaguchi

  3. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Taro Takaguchi

  4. Department of Engineering Mathematics, University of Bristol, Woodland Road, Clifton, Bristol, BS8 1UB, UK

    Naoki Masuda

Authors
  1. Leo Speidel
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  2. Taro Takaguchi
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  3. Naoki Masuda
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Corresponding author

Correspondence to Naoki Masuda.

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This article is published with open access at Springerlink.com

Contribution to the Topical Issue “Temporal Network Theory and Applications”, edited by Petter Holme.

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Speidel, L., Takaguchi, T. & Masuda, N. Community detection in directed acyclic graphs. Eur. Phys. J. B 88, 203 (2015). https://doi.org/10.1140/epjb/e2015-60226-y

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  • DOI: https://doi.org/10.1140/epjb/e2015-60226-y

Keywords

  • Null Model
  • Spectral Method
  • Citation Network
  • Directed Network
  • Jaccard Index