Joint Network Topology Inference Via a Shared Graphon Model

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. The proposed joint network and graphon estimation is further enhanced with the introduction of a robust method for noisy graph sampling information. We validate our proposed approach by comparing its performance against competing methods in synthetic and real-world datasets.

Automated summary

In this study, we address the problem of estimating the topology of multiple networks from nodal observations. Using a graphon model, we can infer the joint structure of graphs with different sizes and imprecise alignment. Our approach combines maximum likelihood penalty with graphon estimation schemes to enhance network inference. The proposed method is validated through comparisons with competing methods on synthetic and real-world datasets.