Nearest-neighbour comparisons for uniformly sampled point distributions. Top: example realisation with N = 10 points drawn within a sphere of radius of R = 1.0. The NN graph constructed in 3D (left), its 2D projection obtained by dropping the line-of-sight coordinate (centre), and the corresponding edge-length distributions (right) illustrate how projection systematically shortens apparent separations and modifies the network connectivity even in a simple isotropic configuration. Bottom: results from the Monte Carlo ensembles (10³ realisations each) for N = 5, 10, 20, and 50 showing stacked kernel density estimates of 3D (blue) and projected 2D (orange) NN edge lengths. The distributions converge at a stable median ratio as N increases, while stochastic fluctuations dominate at small values of N.