The graph is the same synthetic quantum-tech collaboration network as the 2D version — a stochastic block model with a handful of hidden "labs" wired with a high intra-lab edge probability and a low inter-lab one — rendered here as spheres in free-orbit 3D space instead of a flat canvas. The community-detection algorithm running underneath is identical and just as real: greedy modularity optimization (Clauset–Newman–Moore).
Q = Σ_c [ L_c/m − (K_c / 2m)² ]
ΔQ(c1,c2) = 2 · [ e(c1,c2)/m − (K_c1/2m)·(K_c2/2m) ]
Every node starts as its own singleton community. At each step the algorithm scans every pair of communities connected by at least one edge, computes the exact ΔQ each merge would produce from the community's tracked internal-edge count L_c, degree sum K_c, and inter-community edge counts, and commits whichever merge gives the largest gain — stopping only when no remaining merge would increase Q. In 3D, nodes that land in the same community feel an extra spring pull toward each other and a mild push away from nodes in different communities, so the abstract merge sequence becomes a visible clustering: watch separate clumps of spheres drift together and lock into distinct clusters as detection converges, and orbit the camera to see the community structure from any angle a flat 2D layout would hide.