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Entropy 2007, 9(2), 73-82; doi:10.3390/e9020073
Article

Entropy Characteristic on Harmonious Unifying Hybrid Preferential Networks

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Received: 27 September 2006 / Accepted: 18 April 2007 / Published: 21 May 2007
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Abstract

Based on the harmonious unifying hybrid preferential model (HUHPM) networkproposed by our group, the entropy characteristic of an un-weighted HUHPM-BA networkand a weighted HUHPM-BBV network are investigated as the total hybrid ratio d/r ischanged. We derive and compute the general relation of the power exponent of the degreedistribution with the entropy by using the Boltzmann-Gibbs entropy (BGS) and the Tsallisnon-extensive entropy (Sq). It is found that the BGS decreases as d/r increases and thecurrent of the BGS along with hybrid ratio d/r or exponent γ of power-law is in agreementbetween numerical simulation and theoretical analysis. The relationship between the Sq andcharacteristic parameter q under different d/r is also given. And the Sq approaches to theBGS when q → 1. These results can provide a better understanding for evolutioncharacteristic in growing complex networks and further applications in networkengineering are of prospective potential.
Keywords: Entropy; harmonious unifying hybrid preferential model; un-weighted network; weighted network Entropy; harmonious unifying hybrid preferential model; un-weighted network; weighted network
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Li, Y.; Fang, J.-Q.; Bi, Q.; Liu, Q. Entropy Characteristic on Harmonious Unifying Hybrid Preferential Networks. Entropy 2007, 9, 73-82.

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