### Abstract

Language | English |
---|---|

Pages | 1-25 |

Number of pages | 24 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2008 |

DOIs | |

Publication status | Published - 13 Mar 2008 |

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### Keywords

- complex network
- the Erdős-Rényi model
- the Barabási-Albert model
- clumpiness
- assortativity

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2008*, 1-25. https://doi.org/10.1088/1742-5468/2008/03/P03008

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*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2008, pp. 1-25. https://doi.org/10.1088/1742-5468/2008/03/P03008

**'Clumpiness' mixing in complex networks.** / Estrada, Ernesto; Hatano, Naomichi; Gutierrez, Amauri; “Ramón y Cajal”, Spain (Funder).

Research output: Contribution to journal › Article

TY - JOUR

T1 - 'Clumpiness' mixing in complex networks

AU - Estrada, Ernesto

AU - Hatano, Naomichi

AU - Gutierrez, Amauri

AU - “Ramón y Cajal”, Spain (Funder)

PY - 2008/3/13

Y1 - 2008/3/13

N2 - Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristics but accounts only for the clumpiness of the central nodes that are directly connected to each other. The clumpiness coefficient defined in the present paper also takes into account the cases where central nodes are separated by few links. The definition is based on the node degrees and the distances between pairs of nodes. The clumpiness coefficient together with the assortativity coefficient can define four classes of networks. Numerical calculations demonstrate that the classification scheme successfully categorize 30 real-world networks into the four classes of clumped assortative, clumped disassortative, loose assortative and loose disassortative networks. The clumpiness coefficient also differentiates the Erdös-Rényi model from the Barabási-Albert model, which the assortativity coefficient could not differentiate. In addition, the bounds of the clumpiness coefficient as well as the relations among the three measures of clumpiness are discussed.

AB - Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristics but accounts only for the clumpiness of the central nodes that are directly connected to each other. The clumpiness coefficient defined in the present paper also takes into account the cases where central nodes are separated by few links. The definition is based on the node degrees and the distances between pairs of nodes. The clumpiness coefficient together with the assortativity coefficient can define four classes of networks. Numerical calculations demonstrate that the classification scheme successfully categorize 30 real-world networks into the four classes of clumped assortative, clumped disassortative, loose assortative and loose disassortative networks. The clumpiness coefficient also differentiates the Erdös-Rényi model from the Barabási-Albert model, which the assortativity coefficient could not differentiate. In addition, the bounds of the clumpiness coefficient as well as the relations among the three measures of clumpiness are discussed.

KW - complex network

KW - the Erdős-Rényi model

KW - the Barabási-Albert model

KW - clumpiness

KW - assortativity

U2 - 10.1088/1742-5468/2008/03/P03008

DO - 10.1088/1742-5468/2008/03/P03008

M3 - Article

VL - 2008

SP - 1

EP - 25

JO - Journal of Statistical Mechanics: Theory and Experiment

T2 - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

ER -