Approximate Conditional Distributions of Distances Between Nodes in a Two-Dimensional Sensor Network

When the authors represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that they may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph, defined to be the number of edges on a shortest path between them. In this paper, they consider a network of sensors placed uniformly at random in a two-dimensional region and study two conditional distributions related to these distances.