# Wireless Network Reliability Analysis for Arbitrary Network Topologies

## TL;DR

This paper analyzes the reliability of wireless networks with arbitrary topologies using graph theory, deriving outage polynomials and key performance metrics like diversity order and coding gain.

## Contribution

It introduces a novel approach linking graph theory with wireless network reliability, providing analytical tools for arbitrary topologies and correlated channels.

## Key findings

- Outage polynomial derivation for arbitrary topologies
- Relationship between max-flow min-cut and performance metrics
- Analytical expressions for diversity order and coding gain

## Abstract

The outage performance of wireless networks with unstructured network topologies is investigated. The network reliability perspective of graph theory is used to obtain the network outage polynomial of generalized wireless networks by enumerating paths and cut-sets of its graph representation for both uncorrelated and correlated wireless channels. A relation is established between the max-flow min-cut theorem and key communication performance indicators. The diversity order is equal to the size of the minimum cut-set between source and destination, and the coding gain is the number of cut-sets with size equal to the minimum cut. An ergodic capacity analysis of networks with arbitrary topologies based on the network outage polynomial is also presented. Numerical results are used to illustrate the technical definitions and verify the derivations.