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A thermostatistical approach to scale-free networks

Author

Listed:
  • João P. da Cruz

    (Closer Consulting Ltd, Knowledge Dock Business Centre, University of East London, 4-6 University Way, London E16 2RD, UK;
    Centro de Física Teórica e Computacional, Universidade de Lisboa, P-1749-016 Lisboa, Portugal)

  • Nuno A. M. Araújo

    (Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal;
    Centro de Física Teórica e Computacional, 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)

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.

Suggested Citation

  • João P. da Cruz & Nuno A. M. Araújo & Frank Raischel & Pedro G. Lind, 2015. "A thermostatistical approach to scale-free networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(06), pages 1-12.
    • Handle: RePEc:wsi:ijmpcx:v:26:y:2015:i:06:n:s0129183115500709
    DOI: 10.1142/S0129183115500709
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    Cited by:

    1. Moghavvemi, Sedigheh & Ormond, Meghann & Musa, Ghazali & Mohamed Isa, Che Ruhana & Thirumoorthi, Thinaranjeney & Bin Mustapha, Mohd Zulkhairi & Kanapathy, Kanagi A./P. & Chiremel Chandy, Jacob John, 2017. "Connecting with prospective medical tourists online: A cross-sectional analysis of private hospital websites promoting medical tourism in India, Malaysia and Thailand," Tourism Management, Elsevier, vol. 58(C), pages 154-163.
    2. Di Marcoberardino, G. & Chiarabaglio, L. & Manzolini, G. & Campanari, S., 2019. "A Techno-economic comparison of micro-cogeneration systems based on polymer electrolyte membrane fuel cell for residential applications," Applied Energy, Elsevier, vol. 239(C), pages 692-705.
    3. Ozcan, Mustafa, 2018. "The role of renewables in increasing Turkey's self-sufficiency in electrical energy," Renewable and Sustainable Energy Reviews, Elsevier, vol. 82(P3), pages 2629-2639.
    4. Blanco, Victor & Holzhauer, Sascha & Brown, Calum & Lagergren, Fredrik & Vulturius, Gregor & Lindeskog, Mats & Rounsevell, Mark D.A., 2017. "The effect of forest owner decision-making, climatic change and societal demands on land-use change and ecosystem service provision in Sweden," Ecosystem Services, Elsevier, vol. 23(C), pages 174-208.
    5. Söder, Lennart & Lund, Peter D. & Koduvere, Hardi & Bolkesjø, Torjus Folsland & Rossebø, Geir Høyvik & Rosenlund-Soysal, Emilie & Skytte, Klaus & Katz, Jonas & Blumberga, Dagnija, 2018. "A review of demand side flexibility potential in Northern Europe," Renewable and Sustainable Energy Reviews, Elsevier, vol. 91(C), pages 654-664.

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