We describe a new approach for dealing with the following central problem in the self-organization of a geometric sensor network: Given a polygonal region R, and a large, dense set of sensor nodes that are scattered uniformly at random in R. There is no central control unit, and nodes can only communicate locally by wireless radio to all other nodes that are within communication radius r, without knowing their coordinates or distances to other nodes. The objective is to develop a simple distributed protocol that allows nodes to identify themselves as being located near the boundary of R and form connected pieces of the boundary. We give a comparison of several centrality measures commonly used in the analysis of social networks and show that restricted stress centrality is particularly suited for geometric networks; we provide mathematical as well as experimental evidence for the quality of this measure.