Greedy Connectivity of Geographically Embedded Graphs

TL;DR

This paper introduces a measure called greedy connectivity for spatially embedded networks, assessing how well local information-based greedy routing can connect nodes despite transmission imperfections, useful for network design.

Contribution

It proposes a new measure of greedy connectivity for geographical networks that considers local routing and transmission imperfections, aiding in optimal network design.

Findings

Greedy connectivity quantifies the efficiency of local routing in spatial networks.

Higher greedy connectivity indicates better reachability despite transmission imperfections.

The measure can guide the design of more robust geographical networks.

Abstract

We introduce a measure of {\em greedy connectivity} for geographical networks (graphs embedded in space) and where the search for connecting paths relies only on local information, such as a node's location and that of its neighbors. Constraints of this type are common in everyday life applications. Greedy connectivity accounts also for imperfect transmission across established links and is larger the higher the proportion of nodes that can be reached from other nodes with a high probability. Greedy connectivity can be used as a criterion for optimal network design.