2003/06/11 by Imre Derényi, Imre Derenyi, Illés J. Farkas +4 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2003.10.083
published as Physica A 334, 583 (2004) · 4 pages, 3 figures, submitted, corrected and added references
arxiv created 2003/06/11 · openalex publication_date 2003/12/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.