On the topological Properties of the One Dimensional Exponential Random   Geometric Graph
  In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph. 
Bhupendra Gupta, Srikanth K. Iyer, D. Manjunath