On the Quality of Wireless Network Connectivity

TL;DR

This paper investigates how to measure the quality of wireless multi-hop network connectivity using probabilistic matrices, proposing the largest eigenvalue as a key metric for assessing connection reliability.

Contribution

It introduces the probabilistic connectivity matrix and demonstrates its properties, highlighting the largest eigenvalue as a novel measure of network connectivity quality.

Findings

Largest eigenvalue correlates with connectivity quality

Probabilistic connectivity matrix has useful mathematical properties

Eigenvalue-based metric complements capacity measures

Abstract

Despite intensive research in the area of network connectivity, there is an important category of problems that remain unsolved: how to measure the quality of connectivity of a wireless multi-hop network which has a realistic number of nodes, not necessarily large enough to warrant the use of asymptotic analysis, and has unreliable connections, reflecting the inherent unreliable characteristics of wireless communications? The quality of connectivity measures how easily and reliably a packet sent by a node can reach another node. It complements the use of \emph{capacity} to measure the quality of a network in saturated traffic scenarios and provides a native measure of the quality of (end-to-end) network connections. In this paper, we explore the use of probabilistic connectivity matrix as a possible tool to measure the quality of network connectivity. Some interesting properties of the probabilistic connectivity matrix and their connections to the quality of connectivity are demonstrated. We argue that the largest eigenvalue of the probabilistic connectivity matrix can serve as a good measure of the quality of network connectivity.