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# 💎 Max Clique

Band 7 — The Neptune transformer. Find the largest complete subgraph.

Vertices: 10 Density: 60%
Ready

### Algorithm: Bron–Kerbosch with Pivot

Recursively grow a clique, use a pivot vertex to prune branches. Choose a vertex from the candidate set that maximizes connections to remaining candidates. O(3^(n/3)) worst case, but prunes effectively on sparse graphs.

### Why This Matters

Max Clique finds the densest community — social networks, protein interactions, and the tightest frequency cluster in the 72-band spectrum. Neptune sees the densest node.