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A thermostatistical approach to scale-free networks

João P. da Cruz, Nuno A. M. Araújo, Frank Raischel and Pedro G. Lind
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João P. da Cruz: Closer Consulting Ltd, Knowledge Dock Business Centre, University of East London, 4-6 University Way, London E16 2RD, UK;
Nuno A. M. Araújo: Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal;
Frank Raischel: Instituto Dom Luiz, Faculdade de Ciências, 1749-016 University of Lisbon, Lisbon, Portugal
Pedro G. Lind: ForWind and Institute of Physics, University of Oldenburg, DE-26111 Oldenburg, Germany

International Journal of Modern Physics C (IJMPC), 2015, vol. 26, issue 06, 1-12

Abstract: We describe an ensemble of growing scale-free networks in an equilibrium framework, providing insight into why the exponent of empirical scale-free networks in nature is typically robust. In an analogy to thermostatistics, to describe the canonical and microcanonical ensembles, we introduce a functional, whose maximum corresponds to a scale-free configuration. We then identify the equivalents to energy, Zeroth-law, entropy and heat capacity for scale-free networks. Discussing the merging of scale-free networks, we also establish an exact relation to predict their final "equilibrium" degree exponent. All analytic results are complemented with Monte Carlo simulations. Our approach illustrates the possibility to apply the tools of equilibrium statistical physics to study the properties of growing networks, and it also supports the recent arguments on the complementarity between equilibrium and nonequilibrium systems.

Keywords: Networks; complex systems; criticality; nonequilibrium systems; 82.75.-k; 05.65.+b; (search for similar items in EconPapers)
Date: 2015
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