Clustering spectrum of scale-free networks

C. Stegehuis, R.W. van der Hofstad, A.J.E.M. Janssen, J.S.H. van Leeuwaarden

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

Real-world networks often have power-law degrees and scale-free properties, such as ultrasmall distances and ultrafast information spreading. In this paper, we study a third universal property: three-point correlations that suppress the creation of triangles and signal the presence of hierarchy. We quantify this property in terms of c(k), the probability that two neighbors of a degree-k node are neighbors themselves. We investigate how the clustering spectrum k↦c(k) scales with k in the hidden-variable model and show that c(k) follows a universal curve that consists of three k ranges where c(k) remains flat, starts declining, and eventually settles on a power-law c(k)∼k^α with α depending on the power law of the degree distribution. We test these results against ten contemporary real-world networks and explain analytically why the universal curve properties only reveal themselves in large networks.
Original languageEnglish
Article number042309
Number of pages15
JournalPhysical Review E
Volume96
DOIs
Publication statusPublished - 2017

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Scale-free Networks
Clustering
Power Law
Hidden Variables
Curve
Degree Distribution
curves
triangles
hierarchies
Triangle
Quantify
Vertex of a graph
Range of data
Model

Cite this

Stegehuis, C. ; van der Hofstad, R.W. ; Janssen, A.J.E.M. ; van Leeuwaarden, J.S.H. / Clustering spectrum of scale-free networks. In: Physical Review E. 2017 ; Vol. 96.
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title = "Clustering spectrum of scale-free networks",
abstract = "Real-world networks often have power-law degrees and scale-free properties, such as ultrasmall distances and ultrafast information spreading. In this paper, we study a third universal property: three-point correlations that suppress the creation of triangles and signal the presence of hierarchy. We quantify this property in terms of c(k), the probability that two neighbors of a degree-k node are neighbors themselves. We investigate how the clustering spectrum k↦c(k) scales with k in the hidden-variable model and show that c(k) follows a universal curve that consists of three k ranges where c(k) remains flat, starts declining, and eventually settles on a power-law c(k)∼k^α with α depending on the power law of the degree distribution. We test these results against ten contemporary real-world networks and explain analytically why the universal curve properties only reveal themselves in large networks.",
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Stegehuis, C, van der Hofstad, RW, Janssen, AJEM & van Leeuwaarden, JSH 2017, 'Clustering spectrum of scale-free networks', Physical Review E, vol. 96, 042309. https://doi.org/10.1103/PhysRevE.96.042309

Clustering spectrum of scale-free networks. / Stegehuis, C.; van der Hofstad, R.W.; Janssen, A.J.E.M.; van Leeuwaarden, J.S.H.

In: Physical Review E, Vol. 96, 042309, 2017.

Research output: Contribution to journal › Article › Academic › peer-review

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T1 - Clustering spectrum of scale-free networks

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AU - Janssen, A.J.E.M.

AU - van Leeuwaarden, J.S.H.

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AB - Real-world networks often have power-law degrees and scale-free properties, such as ultrasmall distances and ultrafast information spreading. In this paper, we study a third universal property: three-point correlations that suppress the creation of triangles and signal the presence of hierarchy. We quantify this property in terms of c(k), the probability that two neighbors of a degree-k node are neighbors themselves. We investigate how the clustering spectrum k↦c(k) scales with k in the hidden-variable model and show that c(k) follows a universal curve that consists of three k ranges where c(k) remains flat, starts declining, and eventually settles on a power-law c(k)∼k^α with α depending on the power law of the degree distribution. We test these results against ten contemporary real-world networks and explain analytically why the universal curve properties only reveal themselves in large networks.

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Stegehuis C, van der Hofstad RW, Janssen AJEM, van Leeuwaarden JSH. Clustering spectrum of scale-free networks. Physical Review E. 2017;96. 042309. https://doi.org/10.1103/PhysRevE.96.042309

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