### Abstract

Original language | English |
---|---|

Pages (from-to) | 155-179 |

Number of pages | 25 |

Journal | Internet mathematics |

Volume | 11 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- EWI-25536
- IR-95514
- METIS-312470

### Cite this

*Internet mathematics*,

*11*(2), 155-179. https://doi.org/10.1080/15427951.2014.927038

}

*Internet mathematics*, vol. 11, no. 2, pp. 155-179. https://doi.org/10.1080/15427951.2014.927038

**Degree-degree dependencies in directed networks with heavy-tailed degrees.** / van der Hoorn, W.L.F.; Litvak, Nelly.

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

TY - JOUR

T1 - Degree-degree dependencies in directed networks with heavy-tailed degrees

AU - van der Hoorn, W.L.F.

AU - Litvak, Nelly

N1 - eemcs-eprint-25536

PY - 2015

Y1 - 2015

N2 - In network theory, Pearson’s correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree sequences. We prove that for graphs where the in- and out-degree sequences satisfy a power law with realistic parameters, Pearson’s correlation coefficients converge to a nonnegative number in the infinite network size limit. We propose alternative measures for degree-degree dependencies in directed networks based on Spearman’s rho and Kendall’s tau. Using examples and calculations on the Wikipedia graphs for nine different languages, we show why these rank correlation measures are more suited for measuring degree assortativity in directed graphs with heavy-tailed degrees.

AB - In network theory, Pearson’s correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree sequences. We prove that for graphs where the in- and out-degree sequences satisfy a power law with realistic parameters, Pearson’s correlation coefficients converge to a nonnegative number in the infinite network size limit. We propose alternative measures for degree-degree dependencies in directed networks based on Spearman’s rho and Kendall’s tau. Using examples and calculations on the Wikipedia graphs for nine different languages, we show why these rank correlation measures are more suited for measuring degree assortativity in directed graphs with heavy-tailed degrees.

KW - EWI-25536

KW - IR-95514

KW - METIS-312470

U2 - 10.1080/15427951.2014.927038

DO - 10.1080/15427951.2014.927038

M3 - Article

VL - 11

SP - 155

EP - 179

JO - Internet mathematics

JF - Internet mathematics

SN - 1542-7951

IS - 2

ER -