# Vertex Nomination Via Seeded Graph Matching

## TL;DR

This paper introduces a scalable vertex nomination method for large networks with overlapping but non-identical vertex sets, using seeded graph matching on local neighborhoods to identify corresponding vertices.

## Contribution

It presents a novel local neighborhood-based vertex nomination approach that efficiently handles large networks by leveraging seed vertices for subgraph matching.

## Key findings

- Effective in large networks where brute-force matching is infeasible
- Successfully applied to simulations and real data examples
- Provides a ranking of candidate vertices based on likelihood of correspondence

## Abstract

Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph matching methods can be applied directly to recover the missing correspondences, herein we present a principled methodology appropriate for situations in which the networks are too large for brute-force graph matching. Our methodology identifies vertices in a local neighborhood of the vertices of interest in the first network that have verifiable corresponding vertices in the second network. Leveraging these known correspondences, referred to as seeds, we match the induced subgraphs in each network generated by the neighborhoods of these verified seeds, and rank the vertices of the second network in terms of the most likely matches to the original vertices of interest. We demonstrate the applicability of our methodology through simulations and real data examples.