The Quality of Sampling from Geographic Networks

We empirically investigate the factors affecting the quality of information obtained by randomly sampling nodes from a network embedded in two-dimensional space. The motivation for this work is that wireless and other physical networks do in fact have embedding of their nodes in space, although analyses of random walks on such networks often only consider the link structure while ignoring node locations. Of independent interest is the measure we propose to evaluate the quality of sampling: the rate of decrease in the area of the largest empty circle remaining.