Degree correlations in scale-free null models

C. Stegehuis

    Research output: Contribution to journalArticleAcademic

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    Abstract

    We study the average nearest neighbor degree $a(k)$ of vertices with degree $k$. In many real-world networks with power-law degree distribution $a(k)$ falls off in $k$, a property ascribed to the constraint that any two vertices are connected by at most one edge. We show that $a(k)$ indeed decays in $k$ in three simple random graph null models with power-law degrees: the erased configuration model, the rank-1 inhomogeneous random graph and the hyperbolic random graph. We consider the large-network limit when the number of nodes $n$ tends to infinity. We find for all three null models that $a(k)$ starts to decay beyond $n^{(\tau-2)/(\tau-1)}$ and then settles on a power law $a(k)\sim k^{\tau-3}$, with $\tau$ the degree exponent.
    Original languageEnglish
    Article number1709.01085
    Number of pages19
    JournalarXiv
    Issue number1709.01085
    Publication statusPublished - 4 Sep 2017

    Bibliographical note

    19 pages, 4 figures

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