From Graph Isoperimetric Inequality to Network Connectivity -- A New Approach

TL;DR

This paper introduces a novel approach linking graph isoperimetric properties to network connectivity, specifically using hypercube isoperimetric characteristics to determine extra connectivity, thus enhancing understanding of network robustness.

Contribution

It establishes the first known relationship between isoperimetric problems and network connectivity, applying this to hypercube networks to determine their extra connectivity.

Findings

Established a relationship between isoperimetric properties and network connectivity.

Used hypercube isoperimetric properties to compute extra connectivity.

Enhanced understanding of network robustness through isoperimetric analysis.

Abstract

We present a new, novel approach to obtaining a network's connectivity. More specifically, we show that there exists a relationship between a network's graph isoperimetric properties and its conditional connectivity. A network's connectivity is the minimum number of nodes, whose removal will cause the network disconnected. It is a basic and important measure for the network's reliability, hence its overall robustness. Several conditional connectivities have been proposed in the past for the purpose of accurately reflecting various realistic network situations, with extra connectivity being one such conditional connectivity. In this paper, we will use isoperimetric properties of the hypercube network to obtain its extra connectivity. The result of the paper for the first time establishes a relationship between the age-old isoperimetric problem and network connectivity.