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

Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model