2010/12/28 by Guoqiang Mao, Brian D. O. Anderson, Mao, Guoqiang +2
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Mobile Ad Hoc Networks #Networking and Internet Architecture (cs.NI) #Stochastic processes and statistical mechanics #cs.IT #cs.NI #math.IT
paper · pdf · doi:10.48550/arxiv.1012.5693
9 pages, to appear in IEEE INFOCOM 2011, Shanghai, China
arxiv created 2010/12/28 · openalex publication_date 2010/12/28 · arxiv updated 2010/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density ρ and a pair of nodes separated by an Euclidean distance x are directly connected with probability g((x)/(rρ)), where g:[0,∞)→[0,1] satisfies three conditions: rotational invariance, non-increasing monotonicity and integral boundedness, rρ=√((logρ+b)/(Cρ)), C=∫\Re2g(\Vert \boldsymbolx\Vert)d\boldsymbolx and b is a constant, independent of the event that another pair of nodes are directly connected. In this paper, we analyze the asymptotic distribution of the number of isolated nodes in the above network using the Chen-Stein technique and the impact of the boundary effect on the number of isolated nodes as ρ→∞. On that basis we derive a necessary condition for the above network to be asymptotically almost surely connected. These results form an important link in expanding recent results on the connectivity of the random geometric graphs from the commonly used unit disk model to the more generic and more practical random connection model.