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

Entropy Characteristic on Harmonious Unifying Hybrid Preferential Networks

1
,
1,* , 1
 and
1
1 China Institute of Atomic Energy, P.O. Box 275-81, Beijing 102413, P. R. ChinaChina Institute of Atomic Energy, P.O. Box 275-81, Beijing 102413, P. R. China 2 Wuhan University of Technology, Wuhan 430070, P. R. China
* Author to whom correspondence should be addressed.
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 (CC BY 3.0).
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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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