Variational principle for scale-free network motifs

Clara Stegehuis (Corresponding author), Remco van der Hofstad, Johan S.H. van Leeuwaarden

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    Abstract

    For scale-free networks with degrees following a power law with an exponent τ ∈ (2, 3), the structures of motifs (small subgraphs) are not yet well understood. We introduce a method designed to identify the dominant structure of any given motif as the solution of an optimization problem. The unique optimizer describes the degrees of the vertices that together span the most likely motif, resulting in explicit asymptotic formulas for the motif count and its fluctuations. We then classify all motifs into two categories: motifs with small and large fluctuations.

    Original languageEnglish
    Article number6762
    Number of pages10
    JournalScientific Reports
    Volume9
    Issue number1
    DOIs
    Publication statusPublished - 1 Dec 2019

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