  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.
