  We consider atoms interacting each other through the topological structure of
a complex network and investigate lattice vibrations of the system, the quanta
of which we call {\em netons} for convenience. The density of neton levels,
obtained numerically, reveals that unlike a local regular lattice, the system
develops a gap of a 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 $r = 1$.
