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Inhomogeneous Long-Range Percolation for Real-Life Network Modeling

Author

Listed:
  • Philippe Deprez

    (RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland)

  • Rajat Subhra Hazra

    (Indian Statistical Institute, Theoretical Statistics and Mathematics Unit, Kolkata 700 108, India)

  • Mario V. Wüthrich

    (RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
    Swiss Finance Institute SFI Professor, 8006 Zurich, Switzerland)

Abstract

The study of random graphs has become very popular for real-life network modeling, such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice Z d , d ≥ 1, is a particular attractive example of a random graph model because it fulfills several stylized facts of real-life networks. For this model, various geometric properties, such as the percolation behavior, the degree distribution and graph distances, have been analyzed. In the present paper, we complement the picture of graph distances and we prove continuity of the percolation probability in the phase transition point. We also provide an illustration of the model connected to financial networks.

Suggested Citation

  • Philippe Deprez & Rajat Subhra Hazra & Mario V. Wüthrich, 2015. "Inhomogeneous Long-Range Percolation for Real-Life Network Modeling," Risks, MDPI, vol. 3(1), pages 1-23, January.
    • Handle: RePEc:gam:jrisks:v:3:y:2015:i:1:p:1-23:d:44286
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    References listed on IDEAS

    as
    1. Soramäki, Kimmo & Bech, Morten L. & Arnold, Jeffrey & Glass, Robert J. & Beyeler, Walter E., 2007. "The topology of interbank payment flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 317-333.
    2. Grilli, Ruggero & Tedeschi, Gabriele & Gallegati, Mauro, 2014. "Bank interlinkages and macroeconomic stability," International Review of Economics & Finance, Elsevier, vol. 34(C), pages 72-88.
    3. Hamed Amini & Rama Cont & Andreea Minca, 2012. "Stress Testing The Resilience Of Financial Networks," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 2, pages 17-36, World Scientific Publishing Co. Pte. Ltd..
    4. Bech, Morten L. & Atalay, Enghin, 2010. "The topology of the federal funds market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5223-5246.
    5. Hamed Amini & Rama Cont & Andreea Minca, 2012. "Stress Testing The Resilience Of Financial Networks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-20.
    6. Hamed Amini & Rama Cont & Andreea Minca, 2012. "Stress testing the resilience of financial networks," Post-Print hal-00801538, HAL.
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    Cited by:

    1. Cipriani, Alessandra & Salvi, Michele, 2024. "Scale-free percolation mixing time," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    2. Jorritsma, Joost & Hulshof, Tim & Komjáthy, Júlia, 2020. "Not all interventions are equal for the height of the second peak," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Komjáthy, Júlia & Lodewijks, Bas, 2020. "Explosion in weighted hyperbolic random graphs and geometric inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1309-1367.

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