Authors:
Villő Csiszár Eötvös Loránd University, Budapest, Hungarye-mails: moritamas@ludens.elte.hu, villo@ludens.elte.hu

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Péter Hussami Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungarye-mails: huprim@yahoo.com, tusnady@renyi.hu

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János Komlós Department of Mathematics, Rutgers University, New Brunswick, New Jersey, USAe-mail: komlos@math.rutgers.edu

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Tamás F. Móri Eötvös Loránd University, Budapest, Hungarye-mails: moritamas@ludens.elte.hu, villo@ludens.elte.hu

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Lídia Rejtő Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungarye-mails: huprim@yahoo.com, tusnady@renyi.hu
Statistics Program, FREC, CANR, University of Delaware, Newark, Delaware, USA

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Gábor Tusnády Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungarye-mails: huprim@yahoo.com, tusnady@renyi.hu

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Abstract

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.

  • [1] Barvinok, A. and Hartigan, J. A., 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.

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  • [2] Barvinok, A. and Hartigan, J. A., The number of graphs and a random graph with a given degree sequence, preprint (2010), http://arxiv.org/abs/1003.0356.

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  • [3] Chatterjee, S., Diaconis, P. and Sly, A., Random graphs with a given degree sequence, preprint (2010, arXiv: http://arxiv.org/abs/1005.1136v3 [math.PR]).

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  • [4] Csiszár, I., Shields, P. 2004 Information theory and statistics: A tutorial Foundations and Trends in Communications and Information Theory 1 4 417528 . now Publishers.

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  • [5] Csiszár, V. 2009 Conditional independence relations and log-linear models for random matchings Acta Math. Hungar. 122 131152 .

  • [6] Csiszár, V., Rejtő, L., Tusnády, G. 2008 Statistical inference on random structures Győri, E. (eds.) et al. Horizon of Combinatorics 3767 .

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  • [7] Erdős, P., Gallai, T. 1960 Graphs with given degrees of vertices Mat. Lapok 11 264274 (in Hungarian).

  • [8] Hussami, P., Statistical inference on random graphs, PhD Thesis, 2010 (submitted to Central European University, Budapest).

  • [9] Koren, M. 1973 Extreme degree sequences of simple graphs J. Combinatorial Theory B 15 213224 .

  • [10] Newman, M., Barabási, A.-L., Watts, D. 2007 The Structure and Dynamics of Networks Princeton Studies in Complexity Princeton University Press.

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  • [11] Sierskma, G., Hoogeveen, H. 1991 Seven criteria for integer sequences being graphic J. Graph Theory 2 223231.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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