An iterative step-function estimator for graphons

Abstract: Exchangeable graphs arise via a sampling procedure from measurable functions known as graphons. A natural estimation problem is how well we can recover a graphon given a single graph sampled from it. One general framework for estimating a graphon uses step-functions obtained by partitioning the nodes of the graph according to some clustering algorithm. We propose an iterative step-function estimator (ISFE) that, given an initial partition, iteratively clusters nodes based on their edge densities with respect to the previous iteration's partition. We analyze ISFE and demonstrate its performance in comparison with other graphon estimation techniques.