To provide a phenomenological theory for the various interesting transitions
in restructuring networks we employ a statistical mechanical approach with
detailed balance satisfied for the transitions between topological states. This
enables us to establish an equivalence between the equilibrium rewiring problem
we consider and the dynamics of a lattice gas on the edge-dual graph of a fully
connected network. By assigning energies to the different network topologies
and defining the appropriate order parameters, we find a rich variety of
topological phase transitions, defined as singular changes in the essential
feature(s) of the global connectivity as a function of a parameter playing the
role of the temperature. In the ``critical point'' scale-free networks can be
recovered.Comment: 4 pages, 3 figures, submitted, corrected and added reference