确定度分布条件下可变同配系数的算法构造与影响分析  

Algorithm design and influence analysis of assortativity changing in given degree distribution

作　　者：李静[1,2] 张洪欣[1,3] 王小娟[1] 金磊[1] 

机构地区：[1]北京邮电大学电子工程学院,北京100876 [2]中国信息安全测评中心,北京100085 [3]安全生产智能监控北京市重点实验室(北京邮电大学),北京100876

出　　处：《物理学报》2016年第9期168-177,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61571063;61472357;61501100;61571059)资助的课题~~

摘　　要：复杂网络是现实中大量节点和边的抽象拓扑,如何揭示网络内部拓扑对网络连通性、脆弱性等特征的影响是当前研究的热点.本文在确定度分布的条件下,根据Newman提出的同配系数的定义分析其影响因素.首先在可变同配系数下分别提出了基于度分布的确定算法和基于概率分布的不确定算法,并分别在三种不同类型的网络(Erd?s-Rényi网络,Barabási-Albert网络,Email真实网络)中验证.实验结果表明:当网络规模达到一定程度时,确定算法优于贪婪算法.以此为基础,分析了同配系数改变时聚类系数的变化,发现两者之间存在关联性,并从网络的微观结构变化中揭示了聚类系数变化的原因.Complex network is the abstract topology of a large number of nodes and edges in reality.How to reveal the influences of internal network topology on network connectivity and vulnerability characteristics is a hotspot of current research.In this paper,we analyze the influence of assortativity according to Newman＇s definition of assortativity in a given degree distribution.To fully understand the influence of assortativity we should change the assortativity to see how the topology of network changes.But we find the existing greedy algorithm cannot improve assortativity effectively.First we put forward a deterministic algorithm based on degree distribution and an uncertain algorithm based on probability distribution to increase assortativity.The deterministic algorithm can create a certain network which has a large assortativity without changing node degree.The uncertain algorithm can increase the assortativity continuously by changing the connection of edges.And the uncertain algorithm creates different graphs each time,so the result of the algorithm is uncertain.Then we test our algorithms on three networks（ER network,BA network,Email network） and compare with greedy algorithm,and the experimental results show that the uncertain algorithm performs better than greedy algorithm in three networks which have a large span of assortativity.And our deterministic algorithm performs well in a real world network.We find that we can increase assortativity coefficient up to 1 in ER network.This is because nodes in the ER network are peer to peer.We can also show that that the assortativity cannot increase up to 1 in some networks because nodes in these networks are not in the same status.Because we obtain a large span of assortativity,we can fully understand the change of network topology.On this basis,we analyze the changes of clustering coefficient when using the uncertain algorithm based on a probability distribution to increase the assortativity.We find that there is a certain correlation between assortativity and

关 键 词：同配系数 度分布 构造算法 聚类系数 

分 类 号：O157.5[理学—数学]