Information-theoretic complexity: degree entropy H = −Σ p_k log p_k, Von Neumann entropy from the graph density matrix ρ = L/Tr(L). Ordered vs random vs scale-free.
Network topology
Degree distribution P(k) and entropy
Network entropy quantifies structural complexity. A regular lattice has low entropy (all nodes identical). A random Erdős-Rényi graph has Poisson degree distribution, intermediate entropy. A scale-free (preferential attachment) network has power-law P(k) with high-degree hubs, intermediate entropy but high Gini inequality. The Von Neumann entropy S = −Tr(ρ log ρ) where ρ = L/Tr(L) treats the network as a quantum system.