Scaling of critical connectivity of mobile ad hoc networks

In this paper, critical global connectivity of mobile ad hoc networks (MANETs) 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 η as a function of occupancy σ 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 η∼f(R^βσ), where R=(r−r₀)∕r₀, r₀ is the length unit of the triangular lattice, and β is the scaling index in the universal function f(x). The model serves as a sort of geometric distance-dependent site percolation on dynamic complex networks. Moreover, near each critical σ_c(r) corresponding to certain transmission range r, there exists a cutoff 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 MANETs.