Distribution of Number of Edges on Surface of a Sphere

Abstract—Abstract—In this article we consider N spherical caps of area 4π p were uniformly distributed over the surface of a unit sphere. We study the random intersection graph  G_N constructed by these caps. We prove that for p =c/N^α , c>0 and α>2   , the number of edges in graph G_N follow the Poisson distribution.

Index Terms—Connectivity distance, edges, spherical caps, wireless LAN, wired LAN.

The authors are with the PDPM IIITDM Jabalpur, M.P., India (e-mail:gupta.bhupendra@gmail.com; lokendra.balyan@gmail.com).

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Cite: Bhupendra Gupta and Lokendra Balyan, "Distribution of Number of Edges on Surface of a Sphere," International Journal of Machine Learning and Computing vol. 2, no. 4, pp. 431-433, 2012.