Higher-Order Graphon Theory: Fluctuations, Degeneracies, and Inference

Understand

Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years.

• Graphons, which are the central objects in graph limit theory, provide a natural way to sample exchangeable random graphs.
• It is well known that network moments (motif/subgraph counts) identify a graphon (up to an isomorphism), hence, understanding the sampling distribution of subgraph counts in random graphs sampled from a graphon is pivotal for nonparametric network inference.
• In this paper, we derive the joint asymptotic distribution of any finite collection of network moments in random graphs sampled from a graphon, that includes both the non-degenerate case (where the distribution is Gaussian) as well as the degenerate case (where the distribution has both Gaussian or non-Gaussian components).