When the spatial networks split?

TL;DR

This paper investigates the critical conditions under which a three-dimensional spatial network of randomly distributed nodes becomes disconnected, analyzing how the critical density scales with the number of nodes, with implications for wearable sensor networks.

Contribution

It provides a numerical analysis of the critical density distribution in 3D spatial networks and reveals how it scales with network size, aiding in network design.

Findings

Critical density increases with network size as N^{0.105}

Probability distribution of critical density analyzed numerically

Results applicable to designing protocols for wearable sensors

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.