互联网宏观拓扑结构中社团特征演化分析及应用
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摘要
在网络对人类社会具有重大影响力的今天,面向互联网的研究一直是学术界的热点问题之一。社团结构是许多实际复杂网络的一个重要特征。了解网络的社团结构有助于人们更深入地认识网络的拓扑性质,对于研究网络的形成和演化也非常重要；寻找和分析社团有助于更好地了解网络的结构；对具有社团结构的复杂网络建模有利于分析社团结构对网络性质和动态特性的影响。因此,对复杂网络的社团结构进行分析和建模是当今一个非常具有挑战性和前景性的研究领域。
本文基于CAIDA (The Cooperative Association for Internet Data Analysis)提供的6000余万条海量样本数据,深入研究了互联网宏观拓扑结构,对互联网宏观拓扑结构中的社团特征进行了深入的分析,并在社会网络的一个典型实例——学生网中进行了应用研究,主要工作如下。
结合目前研究工作的现状,在分别介绍了不同类别拓扑分析技术的主要研究内容与成果之后,分析了互联网的拓扑结构模型,并对各类模型进行了定性比较；详细统计了AS (Autonomous System,自治系统)级Internet拓扑的多种宏观特征,进一步分析了网络连通性与幂律特征,对网络的代表性拓扑特征值进行时序分析,并统计了节点的生存周期,分析了其时效规律,并分析了维持网络连通性及幂律性的主要因素。
定义了社团及社团结构,首次提出并建立了由模块度、节点度、聚集系数、跳数分布、介数分布、富人俱乐部连通特性、社团规模分布等多项指标组成的网络社团特征评价体系。
采用模块度分裂曲线对规则网络、随机网络、小世界网络、无尺度网络等几种常见网络的社团特性进行了深入的分析。总结出社团结构是网络的基本特征,深入分析了模块度指标受到网络稀疏程度的影响,并探讨了社团结构与复杂网络特征之间的关系。
基于模块度指标,对互联网宏观拓扑结构的社团特征进行了详细的分析和研究,分析结果显示,互联网拓扑的模块度在0.40左右,这表明互联网拓扑也是具有社团结构的网络。
通过对互联网宏观拓扑的社团结构成因分析发现,处于同一个社团内的AS大多属于相同或者邻近的国家,揭示了地理因素是互联网的社团结构形成的一个重要原因。对互联网国家级拓扑的社团分析显示,互联网国家级拓扑的几个主要社团正好对应到世界的几个主要大洲,进一步说明了地理因素对互联网结构的影响。
综合度优先和社团规模优先的选择机制,提出了一类基于地理演化的具有社团结构的互联网拓扑演化模型——CGeoPFP模型,并应用网络社团特征评价指标对CGeoPFP模型生成的社团进行了演化分析。相关研究结果表明,利用该模型生成的网络,社团规模的累积分布和节点度分布等都满足幂律特征。
相关研究表明,多数社会网络表现出社团结构。作为社会网络的一个重要的部分,大学生群体是一个非常重要的社会网络单元,对大学生社会网络的研究,对于新时期高素质创新型人才的培养、大学生综合素质的养成、大学生思想政治工作的顺利开展等都是十分必要的。本文构建了一个社会网络的典型实例——学生网,建立了学生网络拓扑模型,提出了一类自适应遗传模拟退火算法对模型进行优化,分析了学生网增长的分形特征,研究了学生网增长态势。最后利用社团特征评价指标对学生网的社团特征进行了分析。
Nowadays internet has become one of hottest research spots for a long time since to some extent it has a significant influence on human behavior in modern society.
As the community structure is an important feature in the practical complex network system, thus understanding the community structure is helpful to understand the network topology property better. And it is also valuable to study the formulation and evolvement of the network. As searching and analyzing the community structure is helpful for good acquaintance of network structure, and modeling the complex network with community structure is beneficial to analyze the effect of community structure on network properties and dynamic performance, therefore, analyzing and modeling of the complex network's community structure is a challenging and prospective area.
In this thesis, internet macro topology structure and its community property are analyzed, based on a massive amount of data nearly 60 million provided by CAIDA(The Cooperative Association for Internet Data Analysis). The results are furthermore implemented on a typical student network. The tasks are as follows.
Based on current research, after introducing main content and results of different sorts of topology analysis techniques respectively, the internet topology structure model is analyzed, and a qualitative comparison on various models is carried out. Then the detailed statistics of various internet topology properties on AS(Autonomous System) class is indicated. After that a further analysis on network connectivity property and power-law distribution property is given. The timing analysis of network representative topology eigenvalue is also made, followed by the statistics of node life cycle and analysis of its aging law. The main factors of maintaining the network connectivity and power-law are finally listed.
Definition of community and its structure are specified. Then the evaluation system of the network community property is proposed for the first time, consist of modularity, node degree, clustering coefficient, hop distribution, betweenness distribution, rich-club connection property, community scale distribution, etc.
A deep analysis on some common network community ordinary properties including regular network, random network, small-world network and scale-free network, etc, is made by modularity splitting curve, and by which a conclusion is drawn that the community is one of the basic properties of network. It is also suggested that the modularity is effected by the density of network, and then a deep analysis on the relationship of community structure and complex network is presented.
On the basis of modularity index, by analysis and study of the internet maro topology structure's community property, it can be concluded that the modularity of the internet topology is centered around 0.40, which indicates that the internet topology is also a sort of network with community structure.
By analyzing the cause of the formulation of the internet macro topology's community structure, it shows that Autonomous System from one community mostly belong to the same country or adjacent countries, which reveals that geographical factor is a key influencing factor in internet community structure formulation. The results of analysis on the country-level topology community structure shows us that the main country-level communities internet topology just correspond to the main continents, which again is the evidence of aforementioned geographical influencing theory.
By comprehensive use of degree first selection mechanism and community scale first selection mechanism, a sort of internet topology evolvement model—CGeoPFP model, which has community structure and is built on geographical evolvement theory, is proposed. Then by applying network community property evaluation index, the evolvement analysis of the community generated from CGeoPFP model is given. Its study results shows that if the network generated from this model, its community scale's cumulative distribution and node degree distribution both satisfy power-law property
Relevant studies show that most community networks have community structure. University student as an important part of society network, is also a vital society network cell. The study of university student society network is significant to cultivation of high-quality innovative talents in new era, formulation of university student's comprehensive quality, and development of the ideological and political education. This thesis presents a typical example in the society network-----student network. A student network topology model is built up, and a genetic algorithm and simulated annealing algorithm is utilized for model optimization, by which the student network growth's fractal characteristics and posture are analyzed. Finally, by utilizing community property evaluation index, the community property of student network is analyzed.
本文基于CAIDA (The Cooperative Association for Internet Data Analysis)提供的6000余万条海量样本数据,深入研究了互联网宏观拓扑结构,对互联网宏观拓扑结构中的社团特征进行了深入的分析,并在社会网络的一个典型实例——学生网中进行了应用研究,主要工作如下。
结合目前研究工作的现状,在分别介绍了不同类别拓扑分析技术的主要研究内容与成果之后,分析了互联网的拓扑结构模型,并对各类模型进行了定性比较；详细统计了AS (Autonomous System,自治系统)级Internet拓扑的多种宏观特征,进一步分析了网络连通性与幂律特征,对网络的代表性拓扑特征值进行时序分析,并统计了节点的生存周期,分析了其时效规律,并分析了维持网络连通性及幂律性的主要因素。
定义了社团及社团结构,首次提出并建立了由模块度、节点度、聚集系数、跳数分布、介数分布、富人俱乐部连通特性、社团规模分布等多项指标组成的网络社团特征评价体系。
采用模块度分裂曲线对规则网络、随机网络、小世界网络、无尺度网络等几种常见网络的社团特性进行了深入的分析。总结出社团结构是网络的基本特征,深入分析了模块度指标受到网络稀疏程度的影响,并探讨了社团结构与复杂网络特征之间的关系。
基于模块度指标,对互联网宏观拓扑结构的社团特征进行了详细的分析和研究,分析结果显示,互联网拓扑的模块度在0.40左右,这表明互联网拓扑也是具有社团结构的网络。
通过对互联网宏观拓扑的社团结构成因分析发现,处于同一个社团内的AS大多属于相同或者邻近的国家,揭示了地理因素是互联网的社团结构形成的一个重要原因。对互联网国家级拓扑的社团分析显示,互联网国家级拓扑的几个主要社团正好对应到世界的几个主要大洲,进一步说明了地理因素对互联网结构的影响。
综合度优先和社团规模优先的选择机制,提出了一类基于地理演化的具有社团结构的互联网拓扑演化模型——CGeoPFP模型,并应用网络社团特征评价指标对CGeoPFP模型生成的社团进行了演化分析。相关研究结果表明,利用该模型生成的网络,社团规模的累积分布和节点度分布等都满足幂律特征。
相关研究表明,多数社会网络表现出社团结构。作为社会网络的一个重要的部分,大学生群体是一个非常重要的社会网络单元,对大学生社会网络的研究,对于新时期高素质创新型人才的培养、大学生综合素质的养成、大学生思想政治工作的顺利开展等都是十分必要的。本文构建了一个社会网络的典型实例——学生网,建立了学生网络拓扑模型,提出了一类自适应遗传模拟退火算法对模型进行优化,分析了学生网增长的分形特征,研究了学生网增长态势。最后利用社团特征评价指标对学生网的社团特征进行了分析。
Nowadays internet has become one of hottest research spots for a long time since to some extent it has a significant influence on human behavior in modern society.
As the community structure is an important feature in the practical complex network system, thus understanding the community structure is helpful to understand the network topology property better. And it is also valuable to study the formulation and evolvement of the network. As searching and analyzing the community structure is helpful for good acquaintance of network structure, and modeling the complex network with community structure is beneficial to analyze the effect of community structure on network properties and dynamic performance, therefore, analyzing and modeling of the complex network's community structure is a challenging and prospective area.
In this thesis, internet macro topology structure and its community property are analyzed, based on a massive amount of data nearly 60 million provided by CAIDA(The Cooperative Association for Internet Data Analysis). The results are furthermore implemented on a typical student network. The tasks are as follows.
Based on current research, after introducing main content and results of different sorts of topology analysis techniques respectively, the internet topology structure model is analyzed, and a qualitative comparison on various models is carried out. Then the detailed statistics of various internet topology properties on AS(Autonomous System) class is indicated. After that a further analysis on network connectivity property and power-law distribution property is given. The timing analysis of network representative topology eigenvalue is also made, followed by the statistics of node life cycle and analysis of its aging law. The main factors of maintaining the network connectivity and power-law are finally listed.
Definition of community and its structure are specified. Then the evaluation system of the network community property is proposed for the first time, consist of modularity, node degree, clustering coefficient, hop distribution, betweenness distribution, rich-club connection property, community scale distribution, etc.
A deep analysis on some common network community ordinary properties including regular network, random network, small-world network and scale-free network, etc, is made by modularity splitting curve, and by which a conclusion is drawn that the community is one of the basic properties of network. It is also suggested that the modularity is effected by the density of network, and then a deep analysis on the relationship of community structure and complex network is presented.
On the basis of modularity index, by analysis and study of the internet maro topology structure's community property, it can be concluded that the modularity of the internet topology is centered around 0.40, which indicates that the internet topology is also a sort of network with community structure.
By analyzing the cause of the formulation of the internet macro topology's community structure, it shows that Autonomous System from one community mostly belong to the same country or adjacent countries, which reveals that geographical factor is a key influencing factor in internet community structure formulation. The results of analysis on the country-level topology community structure shows us that the main country-level communities internet topology just correspond to the main continents, which again is the evidence of aforementioned geographical influencing theory.
By comprehensive use of degree first selection mechanism and community scale first selection mechanism, a sort of internet topology evolvement model—CGeoPFP model, which has community structure and is built on geographical evolvement theory, is proposed. Then by applying network community property evaluation index, the evolvement analysis of the community generated from CGeoPFP model is given. Its study results shows that if the network generated from this model, its community scale's cumulative distribution and node degree distribution both satisfy power-law property
Relevant studies show that most community networks have community structure. University student as an important part of society network, is also a vital society network cell. The study of university student society network is significant to cultivation of high-quality innovative talents in new era, formulation of university student's comprehensive quality, and development of the ideological and political education. This thesis presents a typical example in the society network-----student network. A student network topology model is built up, and a genetic algorithm and simulated annealing algorithm is utilized for model optimization, by which the student network growth's fractal characteristics and posture are analyzed. Finally, by utilizing community property evaluation index, the community property of student network is analyzed.
引文
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