Acta Mathematica Hungarica

, Volume 134, Issue 1–2, pp 45–53 | Cite as

When the degree sequence is a sufficient statistic

  • Villő Csiszár
  • Péter Hussami
  • János Komlós
  • Tamás F. Móri
  • Lídia RejtőEmail author
  • Gábor Tusnády


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.


degree sequence of graphs random graph sufficient statistics maximum likelihood estimation 

2000 Mathematics Subject Classification

62F10 05C07 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  • Villő Csiszár
    • 1
  • Péter Hussami
    • 2
  • János Komlós
    • 3
  • Tamás F. Móri
    • 1
  • Lídia Rejtő
    • 2
    • 4
    Email author
  • Gábor Tusnády
    • 2
  1. 1.Eötvös Loránd UniversityBudapestHungary
  2. 2.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA
  4. 4.Statistics Program, FREC, CANRUniversity of DelawareNewarkUSA

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