When the degree sequence is a sufficient statistic
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There is a uniquely defined random graph model with independent adjacencies in which the degree sequence is a sufficient statistic. The model was recently discovered independently by several authors. Here we join to the statistical investigation of the model, proving that if the degree sequence is in the interior of the polytope defined by the Erdős–Gallai conditions, then a unique maximum likelihood estimate exists.
Keywordsdegree sequence of graphs random graph sufficient statistics maximum likelihood estimation
2000 Mathematics Subject Classification62F10 05C07
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- A. Barvinok and J. A. Hartigan, An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums, preprint (2009), http://arxiv.org/abs/0910.2477.
- A. Barvinok and J. A. Hartigan, The number of graphs and a random graph with a given degree sequence, preprint (2010), http://arxiv.org/abs/1003.0356.
- S. Chatterjee, P. Diaconis and A. Sly, Random graphs with a given degree sequence, preprint (2010, arXiv: 1005.1136v3 [math.PR]).
- P. Erdős and T. Gallai, Graphs with given degrees of vertices, Mat. Lapok, 11 (1960), 264–274 (in Hungarian). Google Scholar
- P. Hussami, Statistical inference on random graphs, PhD Thesis, 2010 (submitted to Central European University, Budapest). Google Scholar
- M. Newman, A.-L. Barabási and D. Watts, The Structure and Dynamics of Networks, Princeton Studies in Complexity, Princeton University Press (2007). Google Scholar
- G. Sierskma and H. Hoogeveen, Seven criteria for integer sequences being graphic, J. Graph Theory, 2 (1991), 223–231. Google Scholar