复合复杂网络模型研究与应用
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摘要
现实世界中的许多复杂系统都可以用复杂网络加以描述。由于复杂系统的结构与功能存在复杂的相互影响,传统的研究大多仅涉及局部子系统；并且,在讨论复杂系统相关性质时,大多仅考虑复杂系统内部单一性质的个体及其相关关系,这些均造成对复杂系统整体描述的困难。因而,研究能够描述复杂系统中多种性质的元素及其相互关系的复杂网络模型,具有重要的理论意义与应用价值。基于此,本文提出了一种复合复杂网络模型,为复杂系统的研究提供了新的研究工具与方法。本文的主要工作如下：
1.提出了一种多子网复合的新型复杂网络模型,该网络模型由若干子网及子网间的连边构成,实现了复杂系统中不同子系统间、不同子系统元素间及同一子系统元素间相互关系的描述。
2.基于上述复合复杂网络模型,给出了相应的模型分析方法。导入网络运算的概念,使得原有的复杂网络性质得以保持,通过引入子网加载函数,简化了复杂系统多子网网络模型构建过程,而子网的退缩函数可以使得观察者将复杂网络的观察限定在某些子网内,从而解决因复杂网络规模过大导致复杂网络性质分析困难的问题,降低了分析的复杂性,为后续复杂系统相关性质的研究提供了理论支持。
3.基于上述复合复杂网络模型和网络运算等定义和定理,由实际问题出发提出两种复杂网络演化模型。针对多子网复合复杂网络存在子系统间交互作用,提出两个子系统复合的复杂网络演化模型,解析计算表明节点度分布符合幂率分布。针对单一性质的节点和边构成的系统,提出一种具有双重连接机制的有限度网络演化模型,模型中节点度因受资源限制,不能无限增长,且节点间具有局部和全局双重连接机制,解析计算结果表明网络中节点度分布服从Mandelbrot分布,与数值仿真结果相符,并且研究了该演化网络的拓扑性质。
4.给出了一种子网间连通系数的指标,用于度量复合复杂网络中子网间的连接紧密程度。将平均路径长度、效率等原有单性质子网的拓扑度量指标拓展到复合复杂网络性质分析中。基于复杂网络上信息传播理论,提出结构向量的概念,用于度量某个节点与网络中其它节点的连接紧密关系,并基于结构向量,提出了一种新的网络社团结构发现算法,相关实验验证了本算法的有效性。
5.基于本文所提的理论模型与相关分析方法,以我国航空与铁路综合交通系统为例,进行了复合复杂网络模型实证研究,通过实证数据分析了我国航空与铁路复合复杂网络的度分布、平均路径长度、效率、子网间连通系数等拓扑性质。并就换乘问题、网络结构脆弱性问题、最优交通工具和路线选择等问题进行了研究,提出了若干有价值的建议。
Many complex systems in nature and human society can be described as complex networks. Complex interaction exists between the structure and function of complex systems. Most of traditional researches only involve local subsystems and signal relationship generated among individuals with same property, which results in a lot of difficult when describing the whole complex network. Thus, researching the network model on how to describe the complex systems in a form with variety of elements and their complex relationships has important theoretical significance and application value. Based on this, this paper studied composite complex network model, providing new research tools and methods to the study of complex systems. The results of innovative research are shown as follows:
1. A composite complex network model is proposed. This model is consists of several sub-networks and their connections. In that form, relationships among different elements in the same complex network, in different complex networks and relationships between different complex networks are given.
2. Based on this new model, analyzing methods are presented. By adopting network computing, intrinsic properties of complex networks is remained. And the problems of existing many difficult in analyzing huge complex network are solved by adopting network computing. By defining function of sub-network, the process of constructing the complex network is simplified. And function of denegation makes observer could analyze this complex network in special sub-network.
3. Based on the above composite complex networks and network operating definitions and theorems, two kinds of network evolution models are proposed from the angle of practical problems. One is evolution model of complex network composing of two sub-systems. Degree distributions in these two models both obey the power law. Another is the model for one subsystem network whose node and links with pure features, its nodes have maximum degree restriction and its nodes links have local and global linkage mechanisms, the theory analysis and numeric simulation all show that its degree distribution obey the Mandelbrot distribution.
4. Connection coefficient focusing on closeness of composite complex network is defined. By adopting propagating mechanism, information vector is given. Based on these definitions a algorithm of detecting community in composite complex network is proposed. The experiments show its validity.
5. For testifying this model, empirical analysis are given by taking airline and railway compositing networks. By statistics analysis, degree distribution, average path length, efficiency and connection coefficient are discussed. In addition, harness of this composite complex network is given. At last, transferring and routing are researched. Several advice are given in order to improve the performance of this transport network.
1.提出了一种多子网复合的新型复杂网络模型,该网络模型由若干子网及子网间的连边构成,实现了复杂系统中不同子系统间、不同子系统元素间及同一子系统元素间相互关系的描述。
2.基于上述复合复杂网络模型,给出了相应的模型分析方法。导入网络运算的概念,使得原有的复杂网络性质得以保持,通过引入子网加载函数,简化了复杂系统多子网网络模型构建过程,而子网的退缩函数可以使得观察者将复杂网络的观察限定在某些子网内,从而解决因复杂网络规模过大导致复杂网络性质分析困难的问题,降低了分析的复杂性,为后续复杂系统相关性质的研究提供了理论支持。
3.基于上述复合复杂网络模型和网络运算等定义和定理,由实际问题出发提出两种复杂网络演化模型。针对多子网复合复杂网络存在子系统间交互作用,提出两个子系统复合的复杂网络演化模型,解析计算表明节点度分布符合幂率分布。针对单一性质的节点和边构成的系统,提出一种具有双重连接机制的有限度网络演化模型,模型中节点度因受资源限制,不能无限增长,且节点间具有局部和全局双重连接机制,解析计算结果表明网络中节点度分布服从Mandelbrot分布,与数值仿真结果相符,并且研究了该演化网络的拓扑性质。
4.给出了一种子网间连通系数的指标,用于度量复合复杂网络中子网间的连接紧密程度。将平均路径长度、效率等原有单性质子网的拓扑度量指标拓展到复合复杂网络性质分析中。基于复杂网络上信息传播理论,提出结构向量的概念,用于度量某个节点与网络中其它节点的连接紧密关系,并基于结构向量,提出了一种新的网络社团结构发现算法,相关实验验证了本算法的有效性。
5.基于本文所提的理论模型与相关分析方法,以我国航空与铁路综合交通系统为例,进行了复合复杂网络模型实证研究,通过实证数据分析了我国航空与铁路复合复杂网络的度分布、平均路径长度、效率、子网间连通系数等拓扑性质。并就换乘问题、网络结构脆弱性问题、最优交通工具和路线选择等问题进行了研究,提出了若干有价值的建议。
Many complex systems in nature and human society can be described as complex networks. Complex interaction exists between the structure and function of complex systems. Most of traditional researches only involve local subsystems and signal relationship generated among individuals with same property, which results in a lot of difficult when describing the whole complex network. Thus, researching the network model on how to describe the complex systems in a form with variety of elements and their complex relationships has important theoretical significance and application value. Based on this, this paper studied composite complex network model, providing new research tools and methods to the study of complex systems. The results of innovative research are shown as follows:
1. A composite complex network model is proposed. This model is consists of several sub-networks and their connections. In that form, relationships among different elements in the same complex network, in different complex networks and relationships between different complex networks are given.
2. Based on this new model, analyzing methods are presented. By adopting network computing, intrinsic properties of complex networks is remained. And the problems of existing many difficult in analyzing huge complex network are solved by adopting network computing. By defining function of sub-network, the process of constructing the complex network is simplified. And function of denegation makes observer could analyze this complex network in special sub-network.
3. Based on the above composite complex networks and network operating definitions and theorems, two kinds of network evolution models are proposed from the angle of practical problems. One is evolution model of complex network composing of two sub-systems. Degree distributions in these two models both obey the power law. Another is the model for one subsystem network whose node and links with pure features, its nodes have maximum degree restriction and its nodes links have local and global linkage mechanisms, the theory analysis and numeric simulation all show that its degree distribution obey the Mandelbrot distribution.
4. Connection coefficient focusing on closeness of composite complex network is defined. By adopting propagating mechanism, information vector is given. Based on these definitions a algorithm of detecting community in composite complex network is proposed. The experiments show its validity.
5. For testifying this model, empirical analysis are given by taking airline and railway compositing networks. By statistics analysis, degree distribution, average path length, efficiency and connection coefficient are discussed. In addition, harness of this composite complex network is given. At last, transferring and routing are researched. Several advice are given in order to improve the performance of this transport network.
引文
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