# Matchability of heterogeneous networks pairs

## TL;DR

This paper investigates the conditions under which heterogeneous networks can be accurately matched, showing that centering techniques like Universal Singular Value Thresholding significantly improve matchability in complex network models.

## Contribution

It introduces a theoretical framework for understanding graph matchability in heterogeneous networks and demonstrates the effectiveness of centering methods like USVT for improving matching accuracy.

## Key findings

- Direct matching often fails in heterogeneous networks
- Centering with USVT restores matchability under mild conditions
- Results validated on real and synthetic data

## Abstract

We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability can be lost with high probability when matching the networks directly. We further demonstrate that under mild model assumptions, matchability is almost perfectly recovered by centering the networks using Universal Singular Value Thresholding before matching. These theoretical results are then demonstrated in both real and synthetic simulation settings. We also recover analogous core-matchability results in a very general core-junk network model, wherein some vertices do not correspond between the graph pair.