A degree-based goodness-of-fit test for heterogeneous random graph models

Sarah Ouadah (1) , Stéphane Robin (1) , Pierre Latouche (2)

1 MIA-Paris - Mathématiques et Informatique Appliquées
2 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

The degree variance has been proposed for many years to study the topology of a network. It can be used to assess the goodness-of-fit of the Erdös-Renyi model. In this paper, we prove the asymptotic normality of the degree variance under this model which enables us to derive a formal test. We generalize this result to the heterogeneous Erdös-Renyi model in which the edges have different respective probabilities to exist. For both models we study the power of the proposed goodness-of-fit test. We also prove the asymptotic normality under specific sparsity regimes. Both tests are illustrated on real networks from social sciences and ecology. Their performances are assessed via a simulation study.

Domaines: Statistiques [math.ST]

Sarah Ouadah, Stéphane Robin, Pierre Latouche. A degree-based goodness-of-fit test for heterogeneous random graph models. 2015. ⟨hal-01187889⟩