Random graph models: an overview of modeling approaches

Channarond, Antoine

Journal de la société française de statistique, Tome 156 (2015) no. 3, pp. 56-94.

Cet article établit une revue non exhaustive des modèles de graphes aléatoires destinés à la modélisation de réseaux d’interaction. Il commence par le modèle d’Erdős-Rényi qui a pu être étudié en profondeur car il repose sur des hypothèses simples d’indépendance et d’homogénéité des liens, cependant trop réductrices pour les applications. L’article se concentre ensuite sur les démarches de modélisation de l’hétérogénéité et des dépendances entre les liens. Il part de modèles probabilistes reproduisant les processus de génération des réseaux réels (modèles de Barabási-Albert ou de Watts-Strogatz par exemple) et arrive à des modèles plus adaptés à la statistique. Les modèles exponentiels (ERGM ou $p^{*}$) permettent d’introduire des dépendances entre les liens voulus. Les modèles à variables latentes permettent de modéliser l’hétérogénéité de la population et de l’analyser.

This article nonexhaustively reviews random graph models designed to model interaction networks. It begins with the Erdős-Rényi model which could be deeply studied, as it is based on simple assumptions: independence and homogeneity of the links. However they are too simplistic for applications. The article then focuses on modeling approaches of the hetereogeneity and of the dependences between the links. It starts from probabilistic models reproducing generative processes of the real-world networks (Barabási-Albert or Watts-Strogatz models for instance) and arrives to models more suitable for statistics. Exponential models (ERGM or $p^{*}$) enable to introduce dependences between the desired links. Models with latent variables enable to model heterogeneity of the population and to analyze it.

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