Dropped Edges and Faces' Size in Gabriel and Relative Neighborhood Graphs

We have developed a mathematical model for calculation of expected value of share of edges being dropped while constructing a Gabriel or a relative neighborhood graph starting from a random geometrical graph created by a homogeneous Poisson point process on a plane. The expressions for the expected values of number of faces and face size are derived as well. All expressions are given as functions of deployment configuration. The results are verified through detailed comparison with extensive simulation results. Since Gabriel and relative neighborhood graphs are used for various applications in ad hoc networking we believe that our model simplifies theoretical analysis of functionality and performance of such networks