搜索
本科毕业论文（2009届）题目杭州公交网络的无标度性实证研究学院理学院专业数学与应用数学班级学号学生姓名指导教师完成日期杭州电子科技大学本科毕业论文摘要复杂网络的无标度性是指网络拓扑结构中边连接的度分布服从幂律分布，而该分布具有标度不变性；其小世界特性是指其网络平均最短路长度与网络规模的对数成比例，且网络聚类系数远大于随机图网络的聚类系数。复杂网络的拓扑特性分析，特别是验证网络的无标度性与小世界特性，对于网络的关键节点发现，网络的抗毁性，网络上信息传播、网络导航等都具有十分重要的理论与现实意义。复杂网络是最近几年新兴的一个研究热点，科学家们发现越来越多的实际网络具有复杂网络的特性，并对复杂网络的模型、容错与抗攻击及其动力学特性做了很多研究。交通网络在实际的生活中有着重要的作用，交通网络的设计、规划与实现对人们出行有着重要的影响。公交网络是交通网络中的重要的组成部分。本文首先介绍了复杂网络的概念及其研究进展，网络演化模型的研究方法，并通过掌握复杂网络获得度分布的三种方法，即速率、主方程、连续理论方法等，分析无标度性与小世界特性的内在形成机理。然后获取杭州公交网络的实际数据，获得网络的度分布，聚类系数，平均最短路长度等拓扑指标，验证网络的无标度性与小世界特性，从而可以根据现有的研究成果针对该网络给出新增公交线路或现有线路改造的合理建议。关键词：无标度网络；小世界特性；聚集性；复杂网络杭州电子科技大学本科毕业论文ABSTRACTThescale-freepropertyofcomplexnetworktopologyreferstothestructureofedge-connecteddegreedistributionobeyspower-lawdistribution,andthedistributionisscaleinvariance.Thesmall-worldnetworkmeansthattheaverageshortestpathlengthisproportiontothenetworksize,andthenetworkclusteringcoefficientismorethanrandomnetworkclusteringcoefficient.Theanalysisoftopologicalpropertiesofcomplexnetwork,especially,scale-freenetworksandsmallworldproperties,hasanimportanttheoreticalandpracticalsignificancetothediscoveryofnetworkhubnodes,networkrobustness,networkinformationspread,andthenetworknavigation,etc.Itisanewresearchhotspotofcomplexnetwork,andmanyscientistshavediscoveredthatmoreandmorereal-worldnetworkshavethepropertyofcomplexnetwork.Manyresearchesaimtothemodelofcomplexnetworks,errortoleration,anddynamicbehavior.Transportnetworkplaysanimportantroleinreallifeandthedesign,planningandrealizationoftransportnetworkhaveanimportantimpacttopeopletransportation.Andpublictransportationnetworkisanimportanttransportnetwork.Firstly,theconceptofcomplexnetworkanditsresearchprogressareintroducedinthispaper.Andtheevolvingnetworkmodelisresearchedandthreemethodsobtainingthedegreedistributionofcomplexnetworks,whicharerateequation,masterequation,andcontinuoustheories,arepresented.Theinherentevolutionmechanismofformingthescale-freeandsmall-worldpropertyisdiscussed.Then,thedataofHangzhoupublictransportationnetworkareaccessedandthedegreedistribution,averageshortestpathlength,andclusteringcoefficientarecalculated.Weverifyscale-freenetworksandsmallworldpropertiestothisnetwork.Sosomereasonableadvicesofincreasingthenewbuslinesorreconstructingtheexistinglinescanbeobtainedbytheresearchresults.Keywords:scale-freenatureof;small-worldcharacteristics;aggregation;complexnetwork杭州电子科技大学本科毕业论文目录1．引言.....................................................................................................................................12．复杂网络的介绍.................................................................................................................22.1复杂网络的发展..........................................................................................................22.2复杂网络的特性..........................................................................................................32.3复杂网络的区分..........................................................................................................32.4复杂网络的研究意义..................................................................................................43．复杂网络的分类.................................................................................................................63.1规则网络......................................................................................................................63.2随机图..........................................................................................................................63.3小世界网络模型..........................................................................................................73.4无标度网络模型..........................................................................................................74．杭州公交网络的建立.........................................................................................................94.1公交网络模型..............................................................................................................94.2杭州公交网络数据描述............................................................................................105．公交网络无标度性...........................................................................................................125.1公交网络的无标度分布............................................................................................125.2公交网络的聚集性....................................................................................................155.3公交网络平均最短路长度与聚类系数....................................................................155.4结果分析....................................................................................................................166．结论...................................................................................................................................19致谢.....................................................................................................................................20参考文献........................................................................................................