  We propose an algorithm for the closed-form recursive computation of joint
moments and cumulants of all orders for k-hop counts in the 1D unit disk random
graph model with Poisson distributed vertices. Our approach uses decompositions
of k-hop counts into multiple Poisson stochastic integrals. As a consequence,
using the Stein method we derive Berry-Esseen bounds for the asymptotic
convergence of renormalized k-hop path counts to the normal distribution as the
density of Poisson vertices tends to infinity. Computer codes for the recursive
symbolic computation of moments and cumulants are provided in appendix.
