基于两种不同择优概率下的无标度网络模型

doi:10.3969/j.issn.1000-5641.2017.06.004

华东师范大学学报(自然科学版) ›› 2017, Vol. 2017 ›› Issue (6): 42-49.doi: 10.3969/j.issn.1000-5641.2017.06.004

基于两种不同择优概率下的无标度网络模型

马飞, 姚兵

西北师范大学数学与统计学院, 兰州 730070

收稿日期:2016-06-01 出版日期:2017-11-25 发布日期:2017-11-25
通讯作者: 姚兵,男,教授,研究方向为图着色与标号以及复杂网络.E-mail:yybb918@163.com E-mail:yybb918@163.com
作者简介:马飞,男,硕士研究生,研究方向为图的标号和复杂网络.E-mail:mafei123987@163.com.
基金资助:
国家自然科学基金（61163054，61363060，61662066）

One scale-free network model based on two different preferential attachment probabilities

MA Fei, YAO Bing

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2016-06-01 Online:2017-11-25 Published:2017-11-25

摘要/Abstract

摘要： 基于标准的无标度网络模型，建立了一般的网络动力系统所符合的偏微分方程，不仅给出无标度网络的一个拓扑性质，而且讨论了其中每个功能函数的实际意义.接着本文扩展了BA网络模型增长的"度优先连接机制"原则，从更一般的情形出发，建立了一类具有2种不同优先连接概率共存的网络模型，通过理论分析，得知该模型具有无标度特性.最后对无标度网络的幂律指数γ的取值范围与多种择优概率并存现象之间的相互关系做了探索，并依据节点在整个网络中的"贡献度"，提出了一类优先连接概率.

关键词: 无标度网络模型, 动态演化, 偏微分方程, 度优先连接, 特殊图形优先连接

Abstract: Based on the classic scale-free network model, we set up the partial differential equation satisfied a more general network dynamic system, and then we not only find another important topological property of scale-free network, but also discuss the real background meaning of every function. Meanwhile, we extend the BA-network-model growth principle, degree-preferential attachment mechanism. Starting from a more general situation, we establish a network model containing degree-preferential attachment probability and special-graph-preferential attachment probability. By analysis, this model is scale-free. Finally, we distinguish the connect between the scope of the power law parameter γ of scale-free network and the phenomena all kinds of preferential attachment probabilities co-existing. According to the contribution level from the vertex to the whole network, we come up with a preferential attachment probability.

Key words: scale-free network model, dynamical evolution, partial differential equation, degree preferential attachment, graph preferential attachment

中图分类号:

O157.5

马飞, 姚兵. 基于两种不同择优概率下的无标度网络模型[J]. 华东师范大学学报(自然科学版), 2017, 2017(6): 42-49.

MA Fei, YAO Bing. One scale-free network model based on two different preferential attachment probabilities[J]. Journal of East China Normal University(Natural Sc, 2017, 2017(6): 42-49.

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基于两种不同择优概率下的无标度网络模型

One scale-free network model based on two different preferential attachment probabilities

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