# Vertex Nomination, Consistent Estimation, and Adversarial Modification

## TL;DR

This paper develops a theoretical framework for vertex nomination, introduces an adversarial contamination model, and proposes a regularization method to improve robustness against network contamination.

## Contribution

It defines Bayes optimality and consistency classes for vertex nomination, and introduces a novel adversarial contamination model with mitigation strategies.

## Key findings

- VN schemes perform well in uncontaminated networks
- Adversarial contamination degrades VN performance
- Regularization improves robustness in contaminated networks

## Abstract

Given a pair of graphs $G_1$ and $G_2$ and a vertex set of interest in $G_1$, the vertex nomination (VN) problem seeks to find the corresponding vertices of interest in $G_2$ (if they exist) and produce a rank list of the vertices in $G_2$, with the corresponding vertices of interest in $G_2$ concentrating, ideally, at the top of the rank list. In this paper, we define and derive the analogue of Bayes optimality for VN with multiple vertices of interest, and we define the notion of maximal consistency classes in vertex nomination. This theory forms the foundation for a novel VN adversarial contamination model, and we demonstrate with real and simulated data that there are VN schemes that perform effectively in the uncontaminated setting, and adversarial network contamination adversely impacts the performance of our VN scheme. We further define a network regularization method for mitigating the impact of the adversarial contamination, and we demonstrate the effectiveness of regularization in both real and synthetic data.