Netons: vibrations of complex networks

We consider atoms interacting with each other through the topological structure of a complex network and investigate lattice vibrations of the system, the quanta of which we call netons for convenience. The density of neton levels, obtained numerically, reveals that unlike a local regular lattice, the system develops a gap of finite width, manifesting extreme rigidity of the network structure at low energies. Two different network models, the small-world network and the scale-free network, are compared: the characteristic structure of the former is described by an additional peak in the level density whereas a power-law tail is observed in the latter, indicating excitability of netons at arbitrarily high energies. The gap width is also found to vanish in the small-world network when the connection range r = 1.