Local clustering in scale-free networks with hidden variables

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Abstract

We investigate the presence of triangles in a class of correlated random graphs in which hidden variables determine the pairwise connections between vertices. The class rules out self-loops and multiple edges. We focus on the regime where the hidden variables follow a power law with exponent τ(2,3), so that the degrees have infinite variance. The natural cutoff hc characterizes the largest degrees in the hidden variable models, and a structural cutoff hs introduces negative degree correlations (disassortative mixing) due to the infinite-variance degrees. We show that local clustering decreases with the hidden variable (or degree). We also determine how the average clustering coefficient C scales with the network size N, as a function of hs and hc. For scale-free networks with exponent 2

Original languageEnglish
Article number022307
Number of pages13
JournalPhysical Review E
Volume95
Issue number2
DOIs
Publication statusPublished - 14 Feb 2017

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Hidden Variables
Scale-free Networks
Clustering
Infinite Variance
cut-off
Exponent
exponents
Clustering Coefficient
Random Graphs
triangles
Pairwise
Triangle
Power Law
apexes
Decrease
coefficients
Class

Cite this

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Local clustering in scale-free networks with hidden variables. / van der Hofstad, R.W.; Janssen, A.J.E.M.; van Leeuwaarden, J.S.H.; Stegehuis, C.

In: Physical Review E, Vol. 95, No. 2, 022307, 14.02.2017.

Research output: Contribution to journalArticleAcademicpeer-review

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