兰州市公交网络的社团结构与脆弱性分析
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摘要
基于复杂网络理论,研究兰州市公交网络的社团结构及其脆弱性.根据实证数据建立了兰州市公交网络的结构模型,并应用Fast Newman算法分析公交网络的社团结构,给出了最优的社团划分;从获得的社团结构出发,分析了兰州市公交网络社团结构的脆弱性,给出了各个社团的脆弱集及脆弱性指标.研究结果表明,兰州市公交网络具有明显的社团结构特性,社团划分受到城市独特地形特性的影响;许多社团在网络中表现异常脆弱,社团之间联系稀疏,极易因为随机故障或蓄意攻击而形成多个独立的连通分支.
The community structure and its vulnerability are investigated for Lanzhou bus transport network based on complex network theory.Firstly,the bus transport network model of Lanzhou City is established based on empirical data,and then its community structure is discussed by use of Fast Newman algorithm,the optimal community division is given.Finally,the vulnerability of Lanzhou bus transport network is analysed from the perspective of the community structure,and the vulnerable set and vulnerability index of every community are determined in detail.The results demonstrate that Lanzhou bus transport network has obvious community structure characteristics,and the community division is influenced by its distinctive urban terrain features;a lot of communities are very weak in the network and the connection between different communities is rather sparse.So the network is fragile under random failures and deliberate attacks,it is very easy to form several independent connected branches.
The community structure and its vulnerability are investigated for Lanzhou bus transport network based on complex network theory.Firstly,the bus transport network model of Lanzhou City is established based on empirical data,and then its community structure is discussed by use of Fast Newman algorithm,the optimal community division is given.Finally,the vulnerability of Lanzhou bus transport network is analysed from the perspective of the community structure,and the vulnerable set and vulnerability index of every community are determined in detail.The results demonstrate that Lanzhou bus transport network has obvious community structure characteristics,and the community division is influenced by its distinctive urban terrain features;a lot of communities are very weak in the network and the connection between different communities is rather sparse.So the network is fragile under random failures and deliberate attacks,it is very easy to form several independent connected branches.
引文
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[2]YANG X H,CHEN G,CHEN S Y,et al.Study on some bus transport networks in China with considering spatial characteristics[J].Transportation Research Part A,2014,69:1.
[3]SEKSAR P,MOHANTY S.An online power system static security assessment module using multilayer perception and radial basis function network[J].Electrical Power and Energy Systems,2016,76:165.
[4]HONG S,YANG Y,ZIO E,et al.A novel dynamics model of fault propagation and equilibrium analysis in complex dynamical communication network[J].Applied Mathematics and Computation,2014,247:1021.
[5]ALBERT R,JEONG H,BARABASI A L.Attack and error tolerance of complex networks[J].Nature,2000,406(6794):387.
[6]LORDAN O,SALLAN J M,SIMO P,et al.Robustness of the air transport network[J].Transportation Research Part E,2014,68(9):155.
[7]CALLAWAY D S,NEWMAN M E J,STROGATZ S H,et al.Network robustness and fragility:percolation on random graphs[J].Physical Review Letters,2000,85(25):5468.
[8]CRUCITTI P,LATORA V,MARCHIORI M,et al.Efficiency of scale-free networks:error and attack tolerance[J].Physica A,2003,320(C):622.
[9]ALBERT R,ALBERT I,NAKARADO G L.Structural vulnerability of the North American power grid[J].Physical Review E,2004,69(2):292.
[10]PETRESKA I,TOMOVSKI I,GUTIERREZ E,et al.Application of modal analysis in assessing attack vulnerability of complex networks[J].Communications in Nonlinear Science&Numerical Simulation,2010,15(4):1008.
[11]BRIN S,PAGE L.The anatomy of a large-scale hypertextual web search engine[J].Computer Networks and ISDN System,1998,30(98):107.
[12]GIRVAN M,NEWMAN M E J.Community structure in social and biological networks[J].Proceedings of the National Academy of Sciences,2002,99(12):7821.
[13]FLAKE G W,LAWRENCE S R,GILES C L,et al.Self-organization and identification of Web communities[J].IEEE Computer,2002,35:66.
[14]KERNIGHAN B W,LIN S.A efficient heuristic procedure for partitioning graphs[J].Bell System Technical Journal,1970,49:291.
[15]POTHEN A,SIMON H,LIOU K P.Partitioning sparse matrices with eigenvectors of graphs[J].SIAM J Matrix Anal Appl,1990,11:430.
[16]BREIGER R L,BOORMAN S A,ARABIE P.An algorithm for clustering relations data with applications to social network analysis and comparison with multidimensional scaling[J].Journal of Mathematical Psychology,1975,12:328.
[17]NEWMAN M E J.Fast algorithm for detecting community structure in networks[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2004,69(6):279.
[18]NEWMAN M E J,GIRVAN M.Finding and evaluating community structure in network[J].Phys Rev E,2004,69:026113.
[19]CLAUDIO M R S,RAMIREZ M J E.Vulnerability metrics and analysis for communities in complex networks[J].Reliability Engineering&System Safety,2011,96(10):1360.