The winner at scale isn't decided by any single value — it's decided by the shape of the curve. Slide N (number of nodes) and watch each topology's diameter and cost grow. N² is a cliff. √N is a slope. log₂N is nearly flat.
Y axis is log-scaled so wildly different sizes fit on one chart. The dashed vertical line marks the N you've selected.
| Topology | Degree | Diameter | Bisection | Cost |
|---|
Read the curves: switch to Cost and slide N up — the crossbar shoots straight up (N²) while mesh, torus and hypercube stay affordable. Switch back to Diameter — mesh and torus climb, but the hypercube barely moves (log₂N). That gap is the whole reason we build the networks we do.