Nonparametric Two-Sample Test for Networks Using Joint Graphon Estimation (2303.16014v1)

Abstract: This paper focuses on the comparison of networks on the basis of statistical inference. For that purpose, we rely on smooth graphon models as a nonparametric modeling strategy that is able to capture complex structural patterns. The graphon itself can be viewed more broadly as density or intensity function on networks, making the model a natural choice for comparison purposes. Extending graphon estimation towards modeling multiple networks simultaneously consequently provides substantial information about the (dis-)similarity between networks. Fitting such a joint model - which can be accomplished by applying an EM-type algorithm - provides a joint graphon estimate plus a corresponding prediction of the node positions for each network. In particular, it entails a generalized network alignment, where nearby nodes play similar structural roles in their respective domains. Given that, we construct a chi-squared test on equivalence of network structures. Simulation studies and real-world examples support the applicability of our network comparison strategy.