### Abstract

Original language | English |
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Article number | 042309 |

Number of pages | 15 |

Journal | Physical Review E |

Volume | 96 |

DOIs | |

Publication status | Published - 2017 |

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*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.

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

TY - JOUR

T1 - Clustering spectrum of scale-free networks

AU - Stegehuis, C.

AU - van der Hofstad, R.W.

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

AU - van Leeuwaarden, J.S.H.

PY - 2017

Y1 - 2017

N2 - 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.

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.

U2 - 10.1103/PhysRevE.96.042309

DO - 10.1103/PhysRevE.96.042309

M3 - Article

C2 - 29347510

VL - 96

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

M1 - 042309

ER -