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Variational principle for scale-free network motifs.

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.

SUBMITTER: Stegehuis C

PROVIDER: S-EPMC6494877 | biostudies-other | 2019 May

REPOSITORIES: biostudies-other

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Variational principle for scale-free network motifs.

Stegehuis Clara C Hofstad Remco van der RV van Leeuwaarden Johan S H JSH

Scientific reports 20190501 1

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 motif ...[more]

PMID: 31043621

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