A random geometric irrigation graph Γn(rn, ξ) has n vertices identified by n independent uniformly distributed points X1, . . . , Xn in the unit square [0, 1]. Each point Xi selects ξi neighbors at random, without replacement, among those points Xj (j 6= i) for which ‖Xi − Xj‖ < rn, and the selected vertices are connected to Xi by an edge. The number ξi of the neighbors is an integer-valued ran...