Acta Mathematica Hungarica

, Volume 134, Issue 1–2, pp 45–53

# When the degree sequence is a sufficient statistic

• Villő Csiszár
• Péter Hussami
• János Komlós
• Tamás F. Móri
• Lídia Rejtő
• Gábor Tusnády
Article

## 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.

## Keywords

degree sequence of graphs random graph sufficient statistics maximum likelihood estimation

62F10 05C07

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## 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