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Graver basis for an undirected graph and its application to testing the beta model of random graphs

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Abstract

In this paper, we give an explicit and algorithmic description of Graver basis for the toric ideal associated with a simple undirected graph and apply the basis for testing the beta model of random graphs by Markov chain Monte Carlo method.

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Mitsunori Ogawa & Akimichi Takemura

  2. Faculty of Economics, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata, 950-2181, Japan

    Hisayuki Hara

  3. JST CREST, 7, Gobancho, Chiyoda-ku, Tokyo, 102-0076, Japan

    Akimichi Takemura

Authors
  1. Mitsunori Ogawa
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  2. Hisayuki Hara
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  3. Akimichi Takemura
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Correspondence to Mitsunori Ogawa.

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Ogawa, M., Hara, H. & Takemura, A. Graver basis for an undirected graph and its application to testing the beta model of random graphs. Ann Inst Stat Math 65, 191–212 (2013). https://doi.org/10.1007/s10463-012-0367-8

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  • DOI: https://doi.org/10.1007/s10463-012-0367-8

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