Model-based graph clustering of a collection of networks using an agglomerative algorithm

Tabea Rebafka (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

Graph clustering is the task of partitioning a collection of observed networks into groups of similar networks. Here similarity means networks have a similar structure or graph topology. To this end, a model-based approach is developed, where the networks are modelled by a finite mixture model of stochastic block models. Moreover, a computationally efficient clustering algorithm is developed. The procedure is an agglomerative hierarchical algorithm that maximizes the so-called integrated classification likelihood criterion. The bottom-up algorithm consists of successive merges of clusters of networks. Those merges require a means to match block labels of two stochastic block models to overcome the label-switching problem. This problem is addressed with a new distance measure for the comparison of stochastic block models based on their graphons. The algorithm provides a cluster hierarchy in form of a dendrogram and valuable estimates of all model parameters.

Mots clés: Graph clustering; multiple networks; stochastic block model; agglomerative algorithm; graphon; integrated classification likelihood; network comparison; node matching; clustering hierarchy

Domaines: Statistiques [math.ST]

Tabea Rebafka. Model-based graph clustering of a collection of networks using an agglomerative algorithm. 2022. ⟨hal-03837505v1⟩