Scaling of critical connectivity of mobile ad hoc communication networks

TL;DR

This paper investigates the critical connectivity behavior of mobile ad hoc networks on a lattice, revealing universal scaling laws and structural properties near percolation thresholds through numerical simulations.

Contribution

It introduces a scaling model for network connectivity based on percolation theory and analyzes structural properties near critical points in mobile ad hoc networks.

Findings

Connectivity scales as a universal function of node density and transmission range.

Near critical points, clustering coefficient remains constant below a cutoff degree.

Average nearest neighbor degree varies linearly with degree near criticality.

Abstract

In this paper, critical global connectivity of mobile ad hoc communication networks (MAHCN) is investigated. We model the two-dimensional plane on which nodes move randomly with a triangular lattice. Demanding the best communication of the network, we account the global connectivity $\eta$ as a function of occupancy $\sigma$ of sites in the lattice by mobile nodes. Critical phenomena of the connectivity for different transmission ranges $r$ are revealed by numerical simulations, and these results fit well to the analysis based on the assumption of homogeneous mixing . Scaling behavior of the connectivity is found as $\eta \sim f(R^{\beta}\sigma)$, where $R=(r-r_{0})/r_{0}$, $r_{0}$ is the length unit of the triangular lattice and $\beta$ is the scaling index in the universal function $f(x)$. The model serves as a sort of site percolation on dynamic complex networks relative to geometric distance. Moreover, near each critical $\sigma_c(r)$ corresponding to certain transmission range $r$, there exists a cut-off degree $k_c$ below which the clustering coefficient of such self-organized networks keeps a constant while the averaged nearest neighbor degree exhibits a unique linear variation with the degree k, which may be useful to the designation of real MAHCN.