When the spatial networks split?

Abstract

We consider a three dimensional spatial network, where $N$ nodes are randomly distributed within a cube $L\times L\times L$. 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 $\rho_c=N(a_c/L)^3$, where one or more nodes become separated; $\rho_c$ 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.