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Degree correlations in directed scale-free networks

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Williams, Oliver and Del Genio, Charo I. (2014) Degree correlations in directed scale-free networks. PLoS One, Volume 9 (Number 10). e110121. doi:10.1371/journal.pone.0110121

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Official URL: http://dx.doi.org/10.1371/journal.pone.0110121

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Abstract

Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which is a measure of the correlation between the degrees of the nodes at the end of the links. Degree correlations are known to affect both the structure of a network and the dynamics of the processes supported thereon, including the resilience to damage, the spread of information and epidemics, and the efficiency of defence mechanisms. Nonetheless, while many studies focus on undirected scale-free networks, the interactions in real-world systems often have a directionality. Here, we investigate the dependence of the degree correlations on the power-law exponents in directed scale-free networks. To perform our study, we consider the problem of building directed networks with a prescribed degree distribution, providing a method for proper generation of power-law-distributed directed degree sequences. Applying this new method, we perform extensive numerical simulations, generating ensembles of directed scale-free networks with exponents between 2 and 3, and measuring ensemble averages of the Pearson correlation coefficients. Our results show that scale-free networks are on average uncorrelated across directed links for three of the four possible degree-degree correlations, namely in-degree to in-degree, in-degree to out-degree, and out-degree to out-degree. However, they exhibit anticorrelation between the number of outgoing connections and the number of incoming ones. The findings are consistent with an entropic origin for the observed disassortativity in biological and technological networks.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science
Faculty of Science, Engineering and Medicine > Science > Mathematics
Faculty of Science, Engineering and Medicine > Science > Physics
Library of Congress Subject Headings (LCSH): System analysis
Journal or Publication Title: PLoS One
Publisher: Public Library of Science
ISSN: 1932-6203
Official Date: 13 October 2014
Dates:
DateEvent
13 October 2014Published
15 September 2014Accepted
22 July 2014Submitted
Volume: Volume 9
Number: Number 10
Number of Pages: 6
Article Number: e110121
DOI: 10.1371/journal.pone.0110121
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
Funder: University of Warwick, Seventh Framework Programme (European Commission) (FP7)
Grant number: 288021 (FP7)

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