Figure 2
From: Scaling in complex systems: a link between the dynamics of networks and growing interfaces
Degree distributions of the natural visibility graphs built from the interfaces at time t = 5000 for the six types of dynamical processes, as obtained by numerical integration of the corresponding continuous master equation for: (EW) Edwards-Wilkinson, (KPZ) Kardar-Parisi-Zhang and (MBE) Molecular Beam Epitaxy and from the simulation of the discrete models: Random Deposition (RD), Random Deposition with Surface Relaxation (RDSR) and Eden model.
As it can be seen, the six degree distributions exhibit a power law dependence but with different exponents. An estimation of the Hurst (α) exponents of each process can be obtained from the exponent of their power law distributions by means of the relation27: 2α = 3 − γ. Concretely, αEW ≈ 0.45, αRDSR ≈ 0.27 αKPZ ≈ 0.47 and αEden ≈ 0.38. The estimation for RD is αRD ≈ 0. Note that the degree distribution of the visibility graph corresponding to MBE presents two regimes for low and large values of k. The first part of the distribution provides αMBE ≈ 1.032, a value that is compatible with the theoretical prediction. The second part of the distribution yields 
, similar to RD. Below each figure the corresponding k-core decomposition of the visibility graph is depicted (see main text).
