@article{(Open Science Index):https://publications.waset.org/pdf/6474,
	  title     = {Topological Properties of an Exponential Random Geometric Graph Process},
	  author    = {Yilun Shang},
	  country	= {},
	  institution	= {},
	  abstract     = {In this paper we consider a one-dimensional random
geometric graph process with the inter-nodal gaps evolving according
to an exponential AR(1) process. The transition probability matrix
and stationary distribution are derived for the Markov chains concerning
connectivity and the number of components. We analyze the
algorithm for hitting time regarding disconnectivity. In addition to
dynamical properties, we also study topological properties for static
snapshots. We obtain the degree distributions as well as asymptotic
precise bounds and strong law of large numbers for connectivity
threshold distance and the largest nearest neighbor distance amongst
others. Both exact results and limit theorems are provided in this
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {5},
	  number    = {4},
	  year      = {2011},
	  pages     = {664 - 669},
	  ee        = {https://publications.waset.org/pdf/6474},
	  url   	= {https://publications.waset.org/vol/52},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 52, 2011},