# The shape of the reliability polynomial of a hammock network

## TL;DR

This paper investigates the reliability polynomial of hammock networks, introducing the concept of X-paths and proving duality properties using topological methods, with implications for network reliability analysis.

## Contribution

It introduces the notion of X-paths and establishes duality properties for hammock networks using the Jordan Curve Theorem, advancing understanding of their reliability polynomials.

## Key findings

- Duality properties for hammock networks established.
- Introduction of X-paths concept for network analysis.
- Implications for reliability polynomial behavior.

## Abstract

Motivated by the study of hammock (aka brick-wall) networks, we introduce in this paper the notion of X-path. Using the Jordan Curve Theorem for piecewise smooth curves, we prove duality properties for hammock networks. Consequences for reliability polynomials are given.