Factorization of network reliability with perfect nodes I: Introduction and statements

TL;DR

This paper introduces a new general theorem for all-terminal network reliability factorization, laying the groundwork for a comprehensive understanding of network robustness.

Contribution

It presents a novel all-terminal network reliability factorization theorem, with detailed proofs to be provided in subsequent work.

Findings

States a new all-terminal network reliability factorization theorem

Lays foundational framework for future proofs and applications

Prepares for detailed proof in subsequent publication

Abstract

A new general all terminal network reliability factorization theorem is stated. We relegate the proof to a forthcoming second part paper.