Natural networks
  Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be expressed in terms of energy. According to the variational principle, the network will grow and restructure when flows of energy diminish energy differences between nodes as well as relative to nodes in surrounding systems. The natural process will yield scale-free characteristics because the nodes that contribute to the least-time consumption of free energy preferably attach to each other. Network evolution is a path-dependent and non-deterministic process when there are two or more paths to consume a common source of energy. Although evolutionary courses of these non-Hamiltonian systems cannot be predicted, many mathematical functions, models and measures that characterize networks can be recognized as appropriate approximations of the thermodynamic equation of motion that has been derived from statistical physics of open systems. 
Tuomo Hartonen and Arto Annila
physics.gen-ph