Topological Properties and Transition Features Generated by a New Hybrid Preferential Model
Fang Jin-Qing, Liang Yong · Chinese Physics Letters · 2005
A new hybrid preferential model (HPM) is proposed for generating both scale-free and small world properties. The topological transition features in the HPM from random preferential attachment to deterministic preferential attachment are investigated. It is found that the exponents γ of the power law are very sensitive to the hybrid ratio ( d / r ) of determination to random attachment, and γ increases as the ratio d / r increases. It is also found that there exists a threshold at d / r = 1/1, beyond which γ increases rapidly and can tend to infinity if there is no random preferential attachment ( r = 0), which implies that the power law scaling disappears completely. Moreover, it is also found that when the ratio d/r increases, the average path length L is decreased, while the average clustering coefficient C is increased. Compared to the BA model and random graph, the new HPM has both the smallest L and the biggest C, which is consistent with most real-world growing networks.