Factorization of network reliability with perfect nodes II: Connectivity matrix

TL;DR

This paper proves a formula for the determinant of the connectivity matrix in network reliability, introducing novel algebraic techniques and connectivity properties, and is a self-contained continuation of prior work.

Contribution

It provides a new algebraic proof of the determinant connectivity matrix formula, expanding theoretical understanding of network reliability matrices.

Findings

Proved the determinant connectivity matrix formula.

Introduced novel algebraic techniques.

Enhanced understanding of connectivity properties in network reliability.

Abstract

We prove the determinant connectivity matrix formula. Mathematically, the proof introduces novel techniques based on an algebraic approach and connectivity properties. Although this is the second part of a previous paper and has its original motivation there, the paper is self contained and the result is interesting in itself.