Large Deviation Principles for Block and Step Graphon Random Graph Models

TL;DR

This paper extends large deviation principles to more general block and step graphon random graph models, providing a broader theoretical framework and simpler formulas for rate functions, with applications to graph sampling.

Contribution

It generalizes previous results by allowing arbitrary block ratios and simplifies the rate function formula, enhancing the theoretical understanding of graphon-based models.

Findings

Established large deviation principles for all block ratios.

Derived a large deviation principle for graph sampling from any step graphon.

Provided a simpler formula for the rate function.

Abstract

Borgs, Chayes, Gaudio, Petti and Sen [arXiv:2007.14508] proved a large deviation principle for block model random graphs with rational block ratios. We strengthen their result by allowing any block ratios (and also establish a simpler formula for the rate function). We apply the new result to derive a large deviation principle for graph sampling from any given step graphon.