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 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 approximately 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 geometric distance-dependent site percolation on dynamic complex networks. Moreover, near each critical sigma_{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.