复杂网络的可达性研究

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摘要

可达性(Accessibility)的概念最早是应用于城市交通规划的研究中，用以作为描

述交通联系程度的指标，这一指标与行程时间或行程距离有关。城市轨道交通的

建设给城市居民的出行提供了很大的方便，节省了时间, 同时为城市建设节省了空

间。但是随着我国城市化进程的加速，轨道交通发展不够成熟，显露出了一些问

题。城市的轨道交通是一个复杂交通运输网络，轨道交通的可达与便利性，需要

考虑在不同的交通时段，网络中各站点能够到达的范围，以及到达目的站点的难

易程度。这其中的相关因素有人流量、线路的拥堵状况以及交通网络中的枢纽站

点的客流量等等。为此，理论的分析城市轨道交通网络的结构特性，对刚刚开始

兴建轨道交通网络的城市对未来的规划具有重要价值。本文以评价复杂网络可达

性度量指标为目的，首先在经典网络和实证网络中进行实验论证其有效性和可行

性，之后以城市轨道交通网络为研究对象，进行了一系列的实验和论证。

首先，介绍并分析对比两种可达性度量模型。在简要分析了对可达性的研究

现状之后，着重介绍了两个经典的可达性度量模型。多样性熵（Diversity Entropy）

的度量是统计在网络中以自避随机游走的方式，在规定的步长下，能够达到其他

节点的概率，它反映的是网络中节点可到达其他区域的多样性；搜索信息（Search

Information）的度量方式是在网络中每一次前进都具体的计算通过每一条边的概率，

以所需信息量

的大小来衡量起始节点的可达性。同时，对比讨论了两种模型，通

过度量实际的网络来深入探讨两种指标在实际网络中的作用效果。

然后，搜索信息度量指标的有效性分析。由于在前面部分只是介绍了该模型

的建模过程，而为了论证搜索信息指标的有效性，并能顺利的用来度量轨道交通

网络，本文分别在随机网络、无标度网络和小世界网络中做了实验分析，实验得

到随机网络的可达性最好，而小世界网络的可达性受初始网络结构和随机断边重

连的概率影响。实验结果显示，断边重连的概率越高或者初始环形网络的连边越

多，可达性越好。随后，又选择了三个实证网络对该指标的有效性进行论证。得

到与实际情况基本符合的结果。由此证明该方法的有效性和可行性。

最后，基于搜索信息指标的上海轨道交通网络可达性分析。以搜索信息的度

量模型为评价工具。分析预测了 2013 年，2020 年和 2030 年上海轨道交通网络的

可达性。根据实验结果，本文分别讨论了三个时期的网络度分布，平均最短路径

条数以及各时期网络与同规模的随机网络的可达性对比。并认为，由于网络规模

较小，2013 年的轨道交通网络更容易被掌握全局信息，于是出现了可达性要高于

后两个时期的现象。并发现在网络规模和复杂性增加的同时，网络连通性和网络

效率并没有增加。城市轨道交通的建设还具有很高的提升空间，提高社会公共建

设、提供方便快捷的交通线路任重而道远。

关键词：可达性轨道交通度分布平均路径条数复杂网络

ABSTRACT

The conception of Accessibility is used as an indicator to illustrate the connections

between transportations in the study of urban traffic planning. This indicator is related

to travel time or travel distance. Accessibility is considered as an important indicator in

the evaluation of the urban traffic network. However, there is a huge difference on sig-

nificance in different fields. The construction of urban rail transit to city residents travel

provides a great convenience, saved more time. At the same time, which saves space for

urban construction. But with the acceleration of urbanization in our country, rail transit

development not mature enough, issues are showing. Urban rail transit is a complex

transportation network, we need to consider in different traffic hours, how far the stop

of the network in the site can reach, and the ease of arrival at the stop. Factors associat-

ed with these traffic line congestion and passenger flow volume in the network hub site

traffic, and so on. For this purpose, the theoretical analysis of the structure characteris-

tics of urban rail transit network has a guiding significance in the initial stage of the

network to enter the city. There is exploratory forward-looking for urban rapid devel-

opment into the network. Based on the evaluation of complex network accessibility

measure, for the purpose of urban rail transit network as the research object, conducted

a series of experiment and demonstration.

Firstly, after analysed and evaluated on the search status of accessibility, we intro-

duced and compared the two classic accessibility measurement model. Diversity entro-

py is a method to count the possibility under a self-avoiding walk with defined steps in

a complex network. Which reflects the diversity of network nodes can be reached in

other area; the other method is Search Information, calculate every possibility of every

way at every step, measure the accessibility of the starting node based on the required

information. At the same time, two models are compared by measuring the actual net-

work to explore its effectiveness.

Secondly, the effectiveness of the Search Information measurement model is ana-

lyzed. In order to demonstrate the validity of the Search Information index, and can be

successfully used to measure the rail transit network, the experimental results respec-

tively in random network , scale-free networks and small-world network have been an-

alyzed. It shows that the accessibility of random network is the best, and the

small-world network will be changed with different initial network structure and the

probability of broken edge rewiring. According to the results, the accessibility is good

only if the high probability or more edges in initial network. After that, three real net-

works are used for analysis of validity. What we get are basically realistic. In conclu-

sion , Search Information is effective and feasible.

Thirdly, accessibility of Shanghai subway transportation network is analyzed.

Based on Search Information method, we analyzed and predicted the Shanghai subway

transportation networks. According to the results, we discussed the degree distribution,

the number of average path length in different periods of the network, at the same time,

they were compared with the same scale ER network on accessibility. Because of

smaller scale, the current network is easier be known, which makes a high accessibility

than other two networks. However, with the increasing scale, network connectivity and

network efficiency are not getting better. The construction of urban subway transporta-

tion also has the very high room to improve, there is still a long way to go on improving

social and public construction and convenient.

Key words: Accessibility, Subway Transportation Networks, Degree

Distribution, the Number of the Average Path Length,

Complex Networks

摘要

ABSTRACT

第一章绪论 .................................................................................................................. 1

1.1 研究背景 .............................................................................................................. 1

1.2 研究意义 .............................................................................................................. 3

1.3 国内外研究现状 .................................................................................................. 3

1.3.1 复杂网络可达性的研究现状 ................................................................. 3

1.3.2 城市交通网络复杂性的研究现状 ......................................................... 6

1.4 本文的主要内容及章节安排 ............................................................................ 11

第二章复杂网络的相关概念 .................................................................................... 12

2.1 经典网络简介 .................................................................................................... 12

2.2 复杂网络的基本拓扑性质 ................................................................................ 13

2.2.1 度和度分布 ........................................................................................... 13

2.2.2 平均最短路径 ....................................................................................... 13

2.2.3 网络效率 ............................................................................................... 14

2.4 本章小结 ............................................................................................................ 14

第三章复杂网络可达性的模型建立 ........................................................................ 15

3.1 可达性的定义 .................................................................................................... 15

3.2 研究网络可达性的两种模型 ............................................................................ 15

3.2.1 多样性熵度量模型 ............................................................................... 15

3.2.2 搜索信息度量模型 ............................................................................... 18

3.3 两种模型的比较 ................................................................................................ 20

3.3.1 对内可达性和对外可达性 ................................................................... 20

3.3.2 到达性和隐藏性 ................................................................................... 20

3.3.3 实验分析 ............................................................................................... 21

3.4 本章小结 ............................................................................................................ 22

第四章搜索信息指标的有效性分析 ........................................................................ 23

4.1 经典网络中的实验分析 .................................................................................... 23

4.1.1 随机网络 ............................................................................................... 23

4.1.2 无标度网络 ........................................................................................... 23

4.1.3 小世界网络 ........................................................................................... 24

4.1.4 网络平均可达性和网络效率的对比 ................................................... 25

4.2 小世界网络结构的变化对可达性的影响 ........................................................ 26

4.2.1 断边重连概率的影响 ........................................................................... 26

4.2.2 初始结构的影响 ................................................................................... 27

4.3 实证分析 ............................................................................................................ 28

4.4 有效性分析 ........................................................................................................ 31

4.5 本章小结 ............................................................................................................ 32

第五章上海轨道交通网络可达性分析 .................................................................... 33

5.1 网络模型构建 .................................................................................................... 33

5.2 可达性分析及网络结构分析 ............................................................................ 34

5.2.1 三个时期可达性值对比 ....................................................................... 34

5.3.2 网络结构分析 ....................................................................................... 36

5.3.3 与随机网络的对比分析 ....................................................................... 38

5.3 本章小结 ............................................................................................................ 38

第六章总结与展望 .................................................................................................... 40

6.1 总结 .................................................................................................................... 40

6.2 展望 .................................................................................................................... 41

参考文献 ...................................................................................................................... 42

在读期间公开发表论文和承担科研项目及取得成果 .............................................. 46

致谢 ............................................................................................................................ 47

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摘要：

摘要可达性(Accessibility)的概念最早是应用于城市交通规划的研究中，用以作为描述交通联系程度的指标，这一指标与行程时间或行程距离有关。城市轨道交通的建设给城市居民的出行提供了很大的方便，节省了时间,同时为城市建设节省了空间。但是随着我国城市化进程的加速，轨道交通发展不够成熟，显露出了一些问题。城市的轨道交通是一个复杂交通运输网络，轨道交通的可达与便利性，需要考虑在不同的交通时段，网络中各站点能够到达的范围，以及到达目的站点的难易程度。这其中的相关因素有人流量、线路的拥堵状况以及交通网络中的枢纽站点的客流量等等。为此，理论的分析城市轨道交通网络的结构特性，对刚刚开始兴建轨道交通网络的...

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