# On the Interplay between Strong Regularity and Graph Densification

## TL;DR

This paper explores how Szemerédi's regularity lemma affects metric information in large graphs, introducing a heuristic for regular partitions that remains robust under graph sparsification and densification.

## Contribution

It presents a heuristic algorithm for finding regular partitions and demonstrates its robustness to graph sparsification and densification effects.

## Key findings

- The heuristic algorithm effectively finds regular partitions in large graphs.
- Regular partitions are robust to graph sparsification.
- Graph densification can enhance the robustness of regular partitions.

## Abstract

In this paper we analyze the practical implications of Szemer\'edi's regularity lemma in the preservation of metric information contained in large graphs. To this end, we present a heuristic algorithm to find regular partitions. Our experiments show that this method is quite robust to the natural sparsification of proximity graphs. In addition, this robustness can be enforced by graph densification.