Nearest-neighbour comparisons for N = 200 points drawn from three centrally concentrated spherical profiles within R = 1.0. Top: Power law with slope p = −2. Middle: truncated Gaussian with σ = 0.25. Bottom: Plummer with scale radius a = 0.25. Each row shows the 3D NN graph (left), the 2D projection (centre), and the corresponding distributions of NN edge lengths (right). Projection shortens apparent separations and rewires most nodes to new, closer neighbours in 2D, with mean ratios ℓ_3D/ℓ_2D ~ 2.3–2.4, well above the geometric baseline 4/π ≃ 1.27.