# Vertex-Connectivity Measures for Node Failure Identification in Boolean Network Tomography

## TL;DR

This paper investigates how vertex connectivity influences node failure detection in undirected graphs using Boolean Network Tomography, providing bounds for specific network classes and analyzing random network models.

## Contribution

It establishes tight bounds on maximal identifiability for Line of Sight networks and explores probabilistic bounds in Erdős-Rényi and Random Regular graphs.

## Key findings

- Tight bounds on maximal identifiability for Line of Sight networks
- Weaker bounds for arbitrary networks
- Probabilistic tradeoff between monitors and identifiability in random networks

## Abstract

In this paper we study the node failure identification problem in undirected graphs by means of Boolean Network Tomography. We argue that vertex connectivity plays a central role. We show tight bounds on the maximal identifiability in a particular class of graphs, the Line of Sight networks. We prove slightly weaker bounds on arbitrary networks. Finally we initiate the study of maximal identifiability in random networks. We focus on two models: the classical Erd\H{o}s-R\'enyi model, and that of Random Regular graphs. The framework proposed in the paper allows a probabilistic analysis of the identifiability in random networks giving a tradeoff between the number of monitors to place and the maximal identifiability.