Stationary Random Graphs with Prescribed Iid Degrees on a Spatial Poisson Process

@inproceedings{Deijfen2008StationaryRG,
title={Stationary Random Graphs with Prescribed Iid Degrees on a Spatial Poisson Process},
author={Maria Deijfen},
year={2008}
}

Let [P ] be the points of a Poisson process on R and F a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant random graphs with vertex set [P ] and iid vertex degrees with distribution F , and the length of the edges is analyzed. The main result is that finite mean for the total edge length per vertex is possible if and only if F has finite moment of order (d + 1)/d.