  The paper tackles the problem of clustering multiple networks, directed or
not, that do not share the same set of vertices, into groups of networks with
similar topology. A statistical model-based approach based on a finite mixture
of stochastic block models is proposed. A clustering is obtained by maximizing
the integrated classification likelihood criterion. This is done by a
hierarchical agglomerative algorithm, that starts from singleton clusters and
successively merges clusters of networks. As such, a sequence of nested
clusterings is computed that can be represented by a dendrogram providing
valuable insights on the collection of networks. Using a Bayesian framework,
model selection is performed in an automated way since the algorithm stops when
the best number of clusters is attained. The algorithm is computationally
efficient, when carefully implemented. The aggregation of clusters requires a
means to overcome the label-switching problem of the stochastic block model and
to match the block labels of the networks. To address this problem, a new tool
is proposed based on a comparison of the graphons of the associated stochastic
block models. The clustering approach is assessed on synthetic data. An
application to a set of ecological networks illustrates the interpretability of
the obtained results.
