'Clumpiness' mixing in complex networks

Ernesto Estrada, Naomichi Hatano, Amauri Gutierrez, “Ramón y Cajal”, Spain (Funder)

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.
LanguageEnglish
Pages1-25
Number of pages24
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2008
DOIs
Publication statusPublished - 13 Mar 2008

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Complex Networks
Coefficient
coefficients
Vertex of a graph
Differentiate
Erdös
Coefficients
Complex networks
Numerical Calculation
Quantify
Node
Model
Demonstrate

Keywords

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

Cite this

Estrada, E., Hatano, N., Gutierrez, A., & “Ramón y Cajal”, Spain (Funder) (2008). 'Clumpiness' mixing in complex networks. Journal of Statistical Mechanics: Theory and Experiment, 2008, 1-25. https://doi.org/10.1088/1742-5468/2008/03/P03008
Estrada, Ernesto ; Hatano, Naomichi ; Gutierrez, Amauri ; “Ramón y Cajal”, Spain (Funder). / 'Clumpiness' mixing in complex networks. In: Journal of Statistical Mechanics: Theory and Experiment. 2008 ; Vol. 2008. pp. 1-25.
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Estrada, E, Hatano, N, Gutierrez, A & “Ramón y Cajal”, Spain (Funder) 2008, ''Clumpiness' mixing in complex networks' 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).

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2008, 13.03.2008, p. 1-25.

Research output: Contribution to journalArticle

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Estrada E, Hatano N, Gutierrez A, “Ramón y Cajal”, Spain (Funder). 'Clumpiness' mixing in complex networks. Journal of Statistical Mechanics: Theory and Experiment. 2008 Mar 13;2008:1-25. https://doi.org/10.1088/1742-5468/2008/03/P03008