Entropy Characteristic on Harmonious Unifying Hybrid

Based on the harmonious unifying hybrid preferential model (HUHPM) network proposed by our group, the entropy characteristic of an un-weighted HUHPM-BA network and a weighted HUHPM-BBV network are investigated as the total hybrid ratio d/r is changed. We derive and compute the general relation of the power exponent of the degree distribution with the entropy by using the Boltzmann-Gibbs entropy (BGS) and the Tsallis non-extensive entropy (Sq). It is found that the BGS decreases as d/r increases and the current of the BGS along with hybrid ratio d/r or exponent γ of power-law is in agreement between numerical simulation and theoretical analysis. The relationship between the Sq and characteristic parameter q under different d/r is also given. And the Sq approaches to the BGS when q→ 1. These results can provide a better understanding for evolution characteristic in growing complex networks and further applications in network engineering are of prospective potential.