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Asymptotic behavior of the node degrees in the ensemble average of adjacency matrix

Published online by Cambridge University Press:  18 July 2016

YUKIO HAYASHI
YUKIO HAYASHI*
Affiliation:
Japan Advanced Institute of Science and Technology, Ishikawa, Japan (e-mail: [email protected])
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Abstract

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Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by the beforehand averaged adjacency matrix over samples of growing networks as a new general framework for investigating the characteristic quantities. It is applied to some network models, and shows a good approximation of degree distribution asymptotically. In particular, our approach will be applicable through the numerical calculations instead of intractable theoretical analyses, when the time-course of degree is a monotone increasing function like power law or logarithm.

Keywords

ensemble averagegrowing networksdegree distributiondegree–degree correlations
Type
Research Article
Information
Network Science , Volume 4 , Issue 3 , September 2016 , pp. 385 - 399
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2016

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