基于向量空间的多子网复合复杂网络模型动态组网运算的形式描述
|
摘要
针对典型复杂网络模型仅描述了复杂系统中同一类个体及其间一种相互关系且对问题的讨论仅局限于同一个系统的问题,基于能够描述复杂系统中异类个体间多种关系的多子网复合复杂网络模型,导入多维向量空间,将网络节点间的关系映射为多维向量,定义了向量复合网.在此基础上,将该模型的动态组网运算(加载与退缩)转化为向量空间的基变换,给出了加载运算与退缩运算的形式描述,实现了多子网复合复杂网络的可计算.建立并分析了我国铁路客运复合网,通过网络动态重组运算,基于高速铁路子网与低速铁路子网的拓扑性质,给出了我国铁路发展现状分析.
Classical complex networks mainly describe same type of entities and one type of interrelations between the entities.Multi-subnet composited network is a model that describes different types of entities and multiple types of interrelations between the entities.Dynamic reorganization of this model provide two operations:Compounding(combine two subnets into a 'bigger' one) and reducing(obtain a 'small' network from a 'big' one).In this paper,a vector-composited network is defined by importing multi-dimensional space,which converts the interrelations between entities into multi-dimensional vector.Dynamic reorganization of networks is converted into base transformations in multi-dimensional space.Formalized descriptions of compounding and reducing are presented.Further,vector-composited network of passenger transport with high speed and low speed railways in mainland China is established by empirical data.Topological analysis of networks obtained by dynamic reorganizations illustrates the development of railway system in mainland China.
Classical complex networks mainly describe same type of entities and one type of interrelations between the entities.Multi-subnet composited network is a model that describes different types of entities and multiple types of interrelations between the entities.Dynamic reorganization of this model provide two operations:Compounding(combine two subnets into a 'bigger' one) and reducing(obtain a 'small' network from a 'big' one).In this paper,a vector-composited network is defined by importing multi-dimensional space,which converts the interrelations between entities into multi-dimensional vector.Dynamic reorganization of networks is converted into base transformations in multi-dimensional space.Formalized descriptions of compounding and reducing are presented.Further,vector-composited network of passenger transport with high speed and low speed railways in mainland China is established by empirical data.Topological analysis of networks obtained by dynamic reorganizations illustrates the development of railway system in mainland China.
引文
[1]Zhang SY.A brief introduction to complex systems and complexity science.Journal of Qingdao University,2001,16(4):25-28(in Chinese with English abstract).
[2]Dai RW.Research on system science and system complexity.Journal of System Simulation,2002,14(ll):1411-1416(in Chinese with English abstract).
[3]Fang JQ.Birth of new science of networks and its development prospects.Journal of Guangxi Normal University:Natural Science Edition,2007,25(3):2-6(in Chinese with English abstract).
[4]Erdos P,Renyi A.On the evolution of random graphs.Bulletin of the International Statistical Institute,1960,38(4):343-347.
[5]Watts DJ,Strogatz SH.Collective dynamics of'small-world'networks.Nature,1998,393:440-442.[doi:10.1038/30918]
[6]Barabasi AL,Albert R.Emergence of scaling in random networks.Science,1999,286:509-512.[doi:10.1126/science.286.5439.509]
[7]Lambiotte R,Ausloos M.Uncovering collective listening habits and music genres in bipartite networks.Physical Review E,2005,72(6):Article 066107.[doi:10.1103/PhysRevE.72.066107]
[8]Goh KI,Cusick ME,Valle D,Childs B,Vidal M,Barabasi AL.The human disease network.Proc.of the National Academy of Sciences,2007,104(21):8685-8690.[doi:10.1073/pnas.0701361104]
[9]Fun CH,Zhang ZP,Chang H,Tao JR,Chen ZH,Dai YL,Zhang W,He DR.A kind of collaboration competition networks.Physica A:Statistical Mechanics and its Applications,2008,387(5-6):1411-1420.[doi:10.1016/j.physa.2007.10.043]
[10]Wu YJ,Zhang P,Di ZR,Fan Y.Study on bipartite networks.Complex Systems and Complexity Science,2010,7(1):l-12(in Chinese with English abstract).
[11]Shang MS,Lu LY,Zhang YC,Zhou T.Empirical analysis of Web-based user-object bipartite networks.Europhysics Letters,2010,90(4):Article 48006.[doi:10.1209/0295-5075/90/48006]
[12]Zhou T,Ren J,Medo M,Zhang YC.Bipartite network projection and personal recommendation.Physical Review E,2007,76:Article 046115.[doi:10.1103/PhysRevE.76.046115]
[13]Zhou T,Jiang LL,Su RQ,Zhang YC.Effect of initial configuration on network-based recommendation.Europhysics Letters,2008,81(5):Article 58004.[doi:10.1209/0295-5075/81/58004]
[14]Lii LY,Zhou T.Link prediction in complex networks:A survey.Physica A:Statistical Mechanics and its Applications,2011,390(6):1150-1170.[doi:10.1016/j.physa.2010.11.027]
[15]Kurant M,Thiran P.Extraction and analysis of traffic and topologies of transportation networks.Physical Review E,2006,74(3):Article 036114.[doi:10.1103/PhysRevE.74.036114]
[16]Kurant M.Layered complex networks.Physical Review Letters,2006,96(13):Article 138701.[doi:10.1103/PhysRevLett.96.138701]
[17]Buldyrev SV,Parshani R,Paul G,Stanley HE,Havlin S.Catastrophic cascade of failures in interdependent networks.Nature,2010,464:1025-1028.[doi:10.1038/nature08932]
[18]Donges JF,Schultz HCH,Marwan N,Zou Y,Kurths J.Investigating the topology of interacting networks.The European Physical Journal B,2011,84:635-651.[doi:10.1140/epjb/e2011-10795-8]
[19]Xu XL,Qu YQ,Guan S,Jiang YM,He DR.Interconnecting bilayer networks.European Physics Letter,2011,93(6):Article68002.[doi:10.1209/0295-5075/93/68002]
[20]Parshani R,Rozenblat C,Ietri D,Ducruet C,Havlin S.Inter-Similarity between coupled networks.Europhyscis Letters,2010,92(6):Article 68002.[doi:10.1209/0295-5075/92/68002]
[21]Yang JM,Wang WJ,Chen GR.A two-level complex network model and its application.Physica A:Statistical Mechanics and its Applications,2009,388(12):2435-2449.[doi:10.1016/j.physa.2009.02.046]
[22]Battiston F,Nicosia V,Latora V.Structural measures for multiplex networks.Physical Review E,2014,89(3):Article 032804.[doi:10.1103/PhysRevE.89.032804]
[23]Cozzo E,Banos RA,Meloni S,Moreno Y.Contact-Based social contagion in multiplex networks.Physical Review E,2013,88(5):Article 050801.[doi:10.1103/PhysRevE.88.050801]
[24]Sergio G,Diaz-Guilera A,Gomez-Gardenes J,Perez-Vicente CJ,Moreno Y,Arenas A.Diffusion dynamics on multiplex networks.Physical Review Letters,2013,110(2):Article 028701.[doi:10.1103/PhysRevLett.110.028701]
[25]Saumell-Mendiola A,Serrano MA,Boguna M.Epidemic spreading on interconnected networks.Physical Review E,2012,86(2):Article 026106.[doi:10.1103/PhysRevE.86.026106]
[26]Gomez-Gardenes J,Reinares I,Arenas A,Floria LM.Evolution of cooperation in multiplex networks.Scientific Reports,2012,2:No.620.
[27]Shao FJ,Sun RC,Li SJ.Multi-Subnetwork composited complex network and its operations.Complex Systems and Complexity Science,2012,9(4):20-25(in Chinese with English abstract).
[28]Shao FJ,Sui Y.Reorganizations of complex networks:Compounding and reducing.Int'l Journal of Modern Physics C,2014,25(5):Article 1440001.[doi:10.1142/S0129183114400014]
[29]Sui Y,Shao FJ,Sun RC,Li JS.Space evolution model and empirical analysis of urban public transport network.Physica A:Statistical Mechanics and its Applications,2012,391(14):3708-3717.[doi:10.1016/j.physa.2012.01.011]
[1]张嗣瀛.复杂系统与复杂性科学简介.青岛大学学报,2001,16(4):25-28.
[2]戴汝为.系统科学与系统复杂性研究.系统仿真学报,2002,14(11):1411-1416.
[3]方锦清.网络科学的诞生与发展前景.广西师范大学学报:自然科学版,2007,25(3):2-6.
[10]吴亚晶,张鹏,狄增如,樊瑛.二分网络研究.复杂系统与复杂性科学,2010,7(1):1-12.
[27]邵峰晶,孙仁诚,李淑静.多子网复合复杂网络及其运算研究.复杂系统与复杂性科学,2012,9(4):20-25.
[2]Dai RW.Research on system science and system complexity.Journal of System Simulation,2002,14(ll):1411-1416(in Chinese with English abstract).
[3]Fang JQ.Birth of new science of networks and its development prospects.Journal of Guangxi Normal University:Natural Science Edition,2007,25(3):2-6(in Chinese with English abstract).
[4]Erdos P,Renyi A.On the evolution of random graphs.Bulletin of the International Statistical Institute,1960,38(4):343-347.
[5]Watts DJ,Strogatz SH.Collective dynamics of'small-world'networks.Nature,1998,393:440-442.[doi:10.1038/30918]
[6]Barabasi AL,Albert R.Emergence of scaling in random networks.Science,1999,286:509-512.[doi:10.1126/science.286.5439.509]
[7]Lambiotte R,Ausloos M.Uncovering collective listening habits and music genres in bipartite networks.Physical Review E,2005,72(6):Article 066107.[doi:10.1103/PhysRevE.72.066107]
[8]Goh KI,Cusick ME,Valle D,Childs B,Vidal M,Barabasi AL.The human disease network.Proc.of the National Academy of Sciences,2007,104(21):8685-8690.[doi:10.1073/pnas.0701361104]
[9]Fun CH,Zhang ZP,Chang H,Tao JR,Chen ZH,Dai YL,Zhang W,He DR.A kind of collaboration competition networks.Physica A:Statistical Mechanics and its Applications,2008,387(5-6):1411-1420.[doi:10.1016/j.physa.2007.10.043]
[10]Wu YJ,Zhang P,Di ZR,Fan Y.Study on bipartite networks.Complex Systems and Complexity Science,2010,7(1):l-12(in Chinese with English abstract).
[11]Shang MS,Lu LY,Zhang YC,Zhou T.Empirical analysis of Web-based user-object bipartite networks.Europhysics Letters,2010,90(4):Article 48006.[doi:10.1209/0295-5075/90/48006]
[12]Zhou T,Ren J,Medo M,Zhang YC.Bipartite network projection and personal recommendation.Physical Review E,2007,76:Article 046115.[doi:10.1103/PhysRevE.76.046115]
[13]Zhou T,Jiang LL,Su RQ,Zhang YC.Effect of initial configuration on network-based recommendation.Europhysics Letters,2008,81(5):Article 58004.[doi:10.1209/0295-5075/81/58004]
[14]Lii LY,Zhou T.Link prediction in complex networks:A survey.Physica A:Statistical Mechanics and its Applications,2011,390(6):1150-1170.[doi:10.1016/j.physa.2010.11.027]
[15]Kurant M,Thiran P.Extraction and analysis of traffic and topologies of transportation networks.Physical Review E,2006,74(3):Article 036114.[doi:10.1103/PhysRevE.74.036114]
[16]Kurant M.Layered complex networks.Physical Review Letters,2006,96(13):Article 138701.[doi:10.1103/PhysRevLett.96.138701]
[17]Buldyrev SV,Parshani R,Paul G,Stanley HE,Havlin S.Catastrophic cascade of failures in interdependent networks.Nature,2010,464:1025-1028.[doi:10.1038/nature08932]
[18]Donges JF,Schultz HCH,Marwan N,Zou Y,Kurths J.Investigating the topology of interacting networks.The European Physical Journal B,2011,84:635-651.[doi:10.1140/epjb/e2011-10795-8]
[19]Xu XL,Qu YQ,Guan S,Jiang YM,He DR.Interconnecting bilayer networks.European Physics Letter,2011,93(6):Article68002.[doi:10.1209/0295-5075/93/68002]
[20]Parshani R,Rozenblat C,Ietri D,Ducruet C,Havlin S.Inter-Similarity between coupled networks.Europhyscis Letters,2010,92(6):Article 68002.[doi:10.1209/0295-5075/92/68002]
[21]Yang JM,Wang WJ,Chen GR.A two-level complex network model and its application.Physica A:Statistical Mechanics and its Applications,2009,388(12):2435-2449.[doi:10.1016/j.physa.2009.02.046]
[22]Battiston F,Nicosia V,Latora V.Structural measures for multiplex networks.Physical Review E,2014,89(3):Article 032804.[doi:10.1103/PhysRevE.89.032804]
[23]Cozzo E,Banos RA,Meloni S,Moreno Y.Contact-Based social contagion in multiplex networks.Physical Review E,2013,88(5):Article 050801.[doi:10.1103/PhysRevE.88.050801]
[24]Sergio G,Diaz-Guilera A,Gomez-Gardenes J,Perez-Vicente CJ,Moreno Y,Arenas A.Diffusion dynamics on multiplex networks.Physical Review Letters,2013,110(2):Article 028701.[doi:10.1103/PhysRevLett.110.028701]
[25]Saumell-Mendiola A,Serrano MA,Boguna M.Epidemic spreading on interconnected networks.Physical Review E,2012,86(2):Article 026106.[doi:10.1103/PhysRevE.86.026106]
[26]Gomez-Gardenes J,Reinares I,Arenas A,Floria LM.Evolution of cooperation in multiplex networks.Scientific Reports,2012,2:No.620.
[27]Shao FJ,Sun RC,Li SJ.Multi-Subnetwork composited complex network and its operations.Complex Systems and Complexity Science,2012,9(4):20-25(in Chinese with English abstract).
[28]Shao FJ,Sui Y.Reorganizations of complex networks:Compounding and reducing.Int'l Journal of Modern Physics C,2014,25(5):Article 1440001.[doi:10.1142/S0129183114400014]
[29]Sui Y,Shao FJ,Sun RC,Li JS.Space evolution model and empirical analysis of urban public transport network.Physica A:Statistical Mechanics and its Applications,2012,391(14):3708-3717.[doi:10.1016/j.physa.2012.01.011]
[1]张嗣瀛.复杂系统与复杂性科学简介.青岛大学学报,2001,16(4):25-28.
[2]戴汝为.系统科学与系统复杂性研究.系统仿真学报,2002,14(11):1411-1416.
[3]方锦清.网络科学的诞生与发展前景.广西师范大学学报:自然科学版,2007,25(3):2-6.
[10]吴亚晶,张鹏,狄增如,樊瑛.二分网络研究.复杂系统与复杂性科学,2010,7(1):1-12.
[27]邵峰晶,孙仁诚,李淑静.多子网复合复杂网络及其运算研究.复杂系统与复杂性科学,2012,9(4):20-25.