High-degree hubs — do they preferentially interconnect?
The rich-club coefficient ρ(k) measures the fraction of edges among nodes with degree > k: ρ(k) = 2E_{>k} / (N_{>k}(N_{>k}−1)). A network has a "rich club" if ρ(k) exceeds that of a random null model. High α biases edges toward high-degree nodes, strengthening the club. Gold nodes = rich-club members (top 20% by degree).