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G. [30]). Local correlation between nodes increases the clustering coefficient [44]. We denote an undirected geometric random graph with N nodes by Gp(rij ) (N ), where p(rij ) is the probability of having a link between two nodes i and j (or j and i) at metric distance rij . We assume in a geometric random graph N nodes are uniformly distributed over the entire service area. This is not an obligatory requirement for the model in general, but it is always assumed to be the case in our study. The reliability of a geometric random graph model depends directly on the accuracy of p(rij ).

As discussed in previous sections, in a wireless ad-hoc network the actual set of connections, in contrast to random graphs or scale-free networks, depends on the geometric distance between nodes. A direct consequence of the dependency of the links on the distance between nodes is that in wireless ad-hoc networks there is an increased probability of two nodes to be connected when they have a common neighbor. In other words, in a wireless ad-hoc network links are locally correlated. g. [30]). Local correlation between nodes increases the clustering coefficient [44].

3) There exists a very close approximation for the mean hopcount given by Hooghiemstra and Van Mieghem ([45], [46]). Although an explanation of the 20 3 Modeling Ad-hoc Networks number of nodes = 500, number of experiments = 1000 16 Albert & Barabasi Newman et. al. 45 4 2 1 2 3 4 5 6 7 Mean degree 8 9 6 10 11 Fig. 3. Comparison of three hopcount formulas with simulated values for a random graph of 500 nodes. Simulation results are average values for 1000 experiments, with standard deviation shown as error bars.

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