The relative neighborhood graph (RNG) of a set S of n points in M.d is a graph (S, E), where (p, q) ∈ E if and only if there is no point z G S such that max{d(p, z), d(q, z)} < d(p, q). We show that in ℝ3, RNG(S) has O(n4/3) edges. We present a randomized algorithm that constructs RNG(S) in expected time O(n3/2+∈) assuming that the points of S are in general position. If the points of S are arbitrary, the expected running time is P(n7/4+∈). These algorithms can be made deterministic without affecting their asymptotic running time.