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

Author

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  • Mitsunori Ogawa
  • Hisayuki Hara
  • Akimichi Takemura

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. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Mitsunori Ogawa & Hisayuki Hara & Akimichi Takemura, 2013. "Graver basis for an undirected graph and its application to testing the beta model of random graphs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 191-212, February.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:1:p:191-212
    DOI: 10.1007/s10463-012-0367-8
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    Cited by:

    1. Elizabeth Gross & Sonja Petrović & Despina Stasi, 2017. "Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 673-704, June.
    2. Abraham Martín del Campo & Sarah Cepeda & Caroline Uhler, 2017. "Exact Goodness-of-Fit Testing for the Ising Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 285-306, June.

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