Topological properties of scale-free networks driven by a graph Hamiltonian

We numerically study an equilibrium network model, generated via a graph Hamiltonian, that exhibits a power-law degree distribution P(k)∼k ^-γ with γ≈1.5 in the thermodynamic limit. While the degree exponent, γ, is equal to the one found in the Merging-Creation (MC) model, we find that the detailed topological properties such as degree-degree correlation and the modular structure differ significantly. We discuss the possible origin of these differences.