Network Renormalization & Coarse-Graining

Real-space RG — merge nodes into supernodes and watch the degree distribution transform

Nodes:
Edges:
RG level: 0
Max degree:
⟨k⟩ =
RG step: merge all nodes sharing an edge (box covering), update edges between supernodes.

Scale-free networks are fixed points: P(k) ~ k−γ preserved under renormalization (Goh et al 2006)
Degree exponent γ ≈