Greedy Connectivity of Geographically Embedded Graphs

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.