点权有限的加权网络演化模型  

An Evolving Model for Weighted Networks with Limited Node Strength

作　　者：刘珊[1] 晏先浩[1] 王仲君[1] 

机构地区：[1]武汉理工大学理学院,武汉430063

出　　处：《复杂系统与复杂性科学》2007年第3期59-65,共7页Complex Systems and Complexity Science

基　　金：国家自然科学基金(70371063)

摘　　要：在BBV(Barrat-Barthélemy-Vespignani)模型的基础上加入节点强度有限限制,即节点强度不允许超过某一定值S,构造了节点强度有限的加权网络演化模型——LBBV模型。理论分析与仿真试验表明,对于3节点的全耦合网络,当S<2mw0时,网络经有限步后演化结束,其结构为同质网络;当S≥2mw0时,LBBV模型的节点强度分布与网络的度分布都呈现幂律分布,并且幂律指数与BBV模型的幂律指数一致,只是相比BBV模型平移了某一常数;当S→∞时,LBBV模型退化为BBV模型。同时通过数值仿真还得到了在不同的S值下、不同规模网络演化后的节点强度分布与度分布都表现出幂律特征,而且幂律指数不随S变化。This paper proposes a new weighted evolving network model （LBBV model） through adding a restricted condition that node strength does not exceed a certain value S based on BBV model. Theoretical analysis and numerical simulation show that for three nodes＇ full couping network, when the limited strength S〈2mwo, the network would evolve into homogeneous network only after a few steps ; when S≥2mwo , the distribution of node strength and node degree of LBBV model are power-law distribution, fur-thermore, the power-law exponent in LBBV is consistent with that in BBV model, which only translate a certain constant compare with BBV model. When S→∞, the LBBV model retrogress into BBV model. From numerical simulation, it shows that with different value of S and different size of network, the distribution of node strength and node degree are power-law after the evolution in LBBV, moreover, the power-law exponent will not change when S alters.

关 键 词：点权有限 加权网络 强度分布 BBV模型 幂律分布 

分 类 号：N94[自然科学总论—系统科学] O24[理学—计算数学]