Rooted motif signatures determine latent position connectivity profiles for generic finite-rank graphons and yield empirical estimators with concentration bounds from a single observed graph.
An iterative step-function estimator for graphons
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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.
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2026 1verdicts
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Beyond Degree: Rooted Motif Signatures for Latent Position Identifiability in Graphon Models
Rooted motif signatures determine latent position connectivity profiles for generic finite-rank graphons and yield empirical estimators with concentration bounds from a single observed graph.