Mao, GuoqiangAnderson, Brian2015-12-100018-9448http://hdl.handle.net/1885/65627This paper studies networks where all nodes are distributed on a unit square Aδ= [-1\2, 1\2]2 following a Poisson distribution with known density rho and a pair of nodes separated by an Euclidean distance x are directly connected with probability grρ(x)Keywords: Boundedness; Connection model; Connectivity; Euclidean distance; Finite order; Isolated nodes; Log-normal model; Monotonicity; Number of components; Random connection models; Random geometric graphs; Rotational invariances; Sufficient and necessary condit Connectivity; random connection model; random geometric graph201310.1109/TIT.2012.22288942016-02-24