Topological phase transitions of random networks

✍ Scribed by Imre Derényi; Illés Farkas; Gergely Palla; Tamás Vicsek

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 223 KB
• Volume: 334
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2003.10.083

✦ Synopsis

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisÿed 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 di erent network topologies and deÿning the appropriate order parameters, we ÿnd a rich variety of topological phase transitions, deÿned 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.