Computing the Probability of Specific Random Sector Graphs with Applications in Wireless Networks with Directional Antennas

A random sector graph ψZ(Xn, r, ?, A) consists of n same size circular sectors with sector degree ?, which uniformly randomly distribute in space A. This kind of graphs is appropriate for modeling an ad hoc wireless sensor network consisting of n mobile devices with a directional antenna that are independently and uniformly distributed randomly in an interested area. Computing sub graph probability in RSGs is shown to be a useful tool for counting the number of induced sub graphs, which explores fairly accurate quantitative property on topology of wireless ad hoc sensor networks. To the best of our knowledge, this work presents the first paradigm to compute the sub graph probability of random sector graphs (with sector degree ? less than 60) in a systematical way.