Local Large deviations for empirical locality measure of typed Random Graph Models

TL;DR

This paper establishes a local large deviation principle for empirical locality measures in typed random graphs, leading to a comprehensive large deviation framework for both typed and Erdős-Rényi graphs without topological restrictions.

Contribution

It introduces a novel LLDP for empirical locality measures in typed random networks, extending large deviation principles to more general graph models.

Findings

LLDP proven for typed random networks conditioned on type and link measures

Full large deviation principle derived for typed and Erdős-Rényi graphs

Results hold without topological restrictions

Abstract

In this article, we prove a local large deviation principle (LLDP) for the empirical locality measure of typed random networks on $n$ nodes conditioned to have a given \emph{ empirical type measure} and \emph{ empirical link measure.} From the LLDP, we deduce a full large deviation principle for the typed random graph, and the classical Erdos-Renyi graphs, where $nc/2$ links are inserted at random among $n$ nodes. No topological restrictions are required for these results.