Probability density function of the euclidean distance between node pairs in rectangular random graphs and its applications in MANETs

This paper focuses on the probability density function of the Euclidean distance between node pairs in rectangular random graphs. As the main achievement of the paper, a closed analytic formula of the probability density function of the Euclidean distance between node pairs in rectangular random graphs was obtained basing on combinatorial theory and asymptotic concept. Some lemmas, such as number of links in fixed radius random graphs, were deduced. These lemmas were also used to get some deductions meaningful to Mobile ad hoc network (MANET) technologies, such as expected number of wireless links, expected node degree, etc. These lemmas were verified through simulations. The results of the paper are suggestive to researches in fields includes MANETs.