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Modern Stochastics: Theory and Applications


Taylor’s power law for the N-stars network evolution model
Volume 6, Issue 3 (2019), pp. 311–331
Pub. online: 16 September 2019      Type: Research Article      Open accessOpen Access
Received
13 March 2019
Revised
9 August 2019
Accepted
9 August 2019
Published
16 September 2019

Abstract

Taylor’s power law states that the variance function decays as a power law. It is observed for population densities of species in ecology. For random networks another power law, that is, the power law degree distribution is widely studied. In this paper the original Taylor’s power law is considered for random networks. A precise mathematical proof is presented that Taylor’s power law is asymptotically true for the N-stars network evolution model.

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Copyright
© 2019 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Taylor’s power law random graph preferential attachment scale free gamma function

MSC2010
05C80 62E10

Funding
The research was supported by the construction EFOP-3.6.3-VEKOP-16-2017-00002; the project was supported by the European Union, co-financed by the European Social Fund.

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