# Universality for critical heavy-tailed network models: Metric structure of maximal components

## TL;DR

This paper investigates the metric structure of the largest components in critical heavy-tailed networks, establishing universal scaling limits and refined asymptotics for susceptibility and diameter across different models.

## Contribution

It develops general principles to extend known results from rank-one inhomogeneous random graphs to broader classes of heavy-tailed network models.

## Key findings

- Identifies universal scaling limits for maximal components
- Provides refined asymptotics for susceptibility functions
- Analyzes the maximal diameter in the barely subcritical regime

## Abstract

We study limits of the largest connected components (viewed as metric spaces) obtained by critical percolation on uniformly chosen graphs and configuration models with heavy-tailed degrees. For rank-one inhomogeneous random graphs, such results were derived by Bhamidi, van der Hofstad, Sen [Probab. Theory Relat. Fields 2018]. We develop general principles under which the identical scaling limits as the rank-one case can be obtained. Of independent interest, we derive refined asymptotics for various susceptibility functions and the maximal diameter in the barely subcritical regime.