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The Emergence of a Giant Component in One-Dimensional Inhomogeneous Networks with Long-Range Effects

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Algorithms and Models for the Web Graph (WAW 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13894))

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Abstract

We study the weight-dependent random connection model, a class of sparse graphs featuring many real-world properties such as heavy-tailed degree distributions and clustering. We introduce a coefficient, \(\delta _\text {eff} \), measuring the effect of the degree-distribution on the occurrence of long edges. We identify a sharp phase transition in \(\delta _\text {eff} \) for the existence of a giant component in dimension \(d=1\).

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Acknowledgement

We gratefully received support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - grant no. 443916008 (SPP 2265) and by the Leibniz Association within the Leibniz Junior Research Group on Probabilistic Methods for Dynamic Communication Networks as part of the Leibniz Competition. We would also like to thank Arne Grauer who provided us the R-code we used for Fig. 2.

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Authors and Affiliations

  1. University of Leeds, Leeds, UK

    Peter Gracar

  2. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Lukas Lüchtrath

  3. Johannes Gutenberg Universität Mainz, Mainz, Germany

    Christian Mönch

Authors
  1. Peter Gracar
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  2. Lukas Lüchtrath
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  3. Christian Mönch
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Correspondence to Lukas Lüchtrath .

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Editors and Affiliations

  1. Tutte Institute for Mathematics and Computing, Ottawa, ON, Canada

    Megan Dewar

  2. Toronto Metropolitan University, Toronto, ON, Canada

    Paweł Prałat

  3. SGH Warsaw School of Economics, Warsaw, Poland

    Przemysław Szufel

  4. Tutte Institute for Mathematics and Computing, Ottawa, ON, Canada

    François Théberge

  5. SGH Warsaw School of Economics, Warsaw, Poland

    Małgorzata Wrzosek

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Gracar, P., Lüchtrath, L., Mönch, C. (2023). The Emergence of a Giant Component in One-Dimensional Inhomogeneous Networks with Long-Range Effects. In: Dewar, M., Prałat, P., Szufel, P., Théberge, F., Wrzosek, M. (eds) Algorithms and Models for the Web Graph. WAW 2023. Lecture Notes in Computer Science, vol 13894. Springer, Cham. https://doi.org/10.1007/978-3-031-32296-9_2

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  • DOI: https://doi.org/10.1007/978-3-031-32296-9_2

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