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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
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 | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science > Centre for Complexity Science Faculty of Science > Mathematics Faculty of Science > Physics |
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| 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: |
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| 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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