Topological phase transitions of random networks

Details Topological phase transitions of random networks Topological phase transitions of random networks

2003-06-06

arxiv.org/abs/cond-mat/0306170v2

Physica A 334, 583 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures, submitted, corrected and added references

Scientific paper

10.1016/j.physa.2003.10.083

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.

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