When the spatial networks split?

Abstract

We consider a three dimensional spatial network, where N nodes are randomly distributed within a cube L×L×L. Each two nodes are connected if their mutual distance does not excess a given cutoff a. We analyse numerically the probability distribution of the critical density , where one or more nodes become separated; ρ c is found to increase with N as N 0.105, where N is between 20 and 300. The results can be useful for a design of protocols to control sets of wearable sensors. © 2008 Springer-Verlag Berlin Heidelberg.