  We consider the problem of estimating the topology of multiple networks from
nodal observations, where these networks are assumed to be drawn from the same
(unknown) random graph model. We adopt a graphon as our random graph model,
which is a nonparametric model from which graphs of potentially different sizes
can be drawn. The versatility of graphons allows us to tackle the joint
inference problem even for the cases where the graphs to be recovered contain
different number of nodes and lack precise alignment across the graphs. Our
solution is based on combining a maximum likelihood penalty with graphon
estimation schemes and can be used to augment existing network inference
methods. We validate our proposed approach by comparing its performance against
competing methods in synthetic and real-world datasets.
