基于中国教育网的网络拓扑结构特性及传播特性研究

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3.0 侯斌 2024-11-19 4 4 1.47MB 50 页 15积分

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摘要

互联网的高速发展为人类的生活和工作带来了深远的影响，在很大程度上改

变了人们获取信息的方式和交流习惯。Web 2.0 技术的出现给互联网带来了深刻的

变革，由最早的博客到后来出现的贴吧、论坛、微博、Facebook、Twitter 等社交工具，

为人们的交流带来了极大的方便，人们利用这些工具可以低成本的维持好友关系

使信息的传播变得比以往任何时候都要迅速。

新技术的出现给互联网用户带来了全新的体验，然而中国教育网作为互联网

的重要组成部分，在中国的教育科研事业中起到了举足轻重的作用，新技术对中

国教育网的拓扑结构产生了怎样的影响，传播源之间的距离对于复杂网络上信息

的传播会产生怎样的影响。针对这两个问题，本文做了一下工作。

首先改写爬虫程序 Heritrix 爬取了中国教育网的数据，计算了中国教育网的

节点度、度分布、群聚系数、度度相关性等网络拓扑结构属性，并与 2004 年和 2007

年的研究结果进行了对比，发现中国教育网的节点平均度呈现出增大的趋势，出

度分布变化明显，已经不服从幂律分布，节点的入度分布服从幂律分布，但入度

指数呈现出减小的趋势。处理中国教育网的数据，得到了有向和无向两个网络，

分别计算了这两个网络的群聚系数，发现有向网络的群聚系数比无向网络的小很

多，但两者均大于之前的研究结果，这表明中国教育网的群聚属性在逐渐增强。

从中国教育网的数据中提取出了单位间的连接关系，构成了校园连接关系网

络。校园连接关系网络的入度分布为幂律分布，幂指数为-0.9，出度分布为双段幂

律分布，第一段幂指数为-1.2，第二段幂指数为-2.1。统计了校园网节点的 k-shell

值以及 k-shell 值分布情况。并考察了节点度、k-shell 值、加权 LeaderRank 三个指标

之间的相关性，发现节点出度、入度、出 k-shell 值和入 k-shell 值四个指标中，节点

的入度在度量节点的重要性方面要优于其他三个指标。校园网络具有较小的平均

最短路径长度和较大的群聚系数，是一个典型的小世界网络。

在校园网、Facebook 和Twitter 网络上考察了传播源距离对于传播效果的影响，

发现在校园网上，并没有明显的影响。Facebook 网络上对于传播能力较弱的节点，

存在一个最优的传播距离，当传播源之间的距离小于最优传播距离时，距离越远

传播效果越好，反之距离越近，传播效果越好。在 Twitter 网络上的实验表明对于

传播能力较强的节点，传播源之间的距离越远，传播效果越好。

关键词:复杂网络中国教育网拓扑结构传播效果距离

ABSTRACT

The rapid development of the Internet has brought the profound

influence to the human’s life and work. It has changed the way people

access to information and communication habits to a great extent. The

advent of Web 2.0 technologies from early blog to Post Bar, forum, micro-

blog, Facebook, Twitter and other social networking tools has brought

profound changes to the Internet. Those make people communicating

conveniently and allow everyone to maintain the relationship with their

friends at low cost. Information is spread very quickly than ever.

The emergency of new technology brings a fresh feeling to users of

Internet. As a part of World Wide Web, China Education Network plays an

important role in Chinese scientific research and education. What is the

impact of new technologies on the topological structure China Education

Network? How is the distance between two initial spreaders affecting the

results of information spreading on complex network? To these two

problems, this thesis has done the following work.

First we crawl China Education Network data by rewriting the crawler

Heritrix. We calculate node degree, degree distribution, clustering

coefficient, degree correlation topological structure properties of that

network. Comparing the results with that of 2004 and 2007 year, the

average degree of nodes tends to increase. Out degree distribution changes

significantly. It does not obey power law distribution. In degree distribution

follows a power-law distribution, but the penetration index tends to

decrease. We acquire two networks by processing the data. One is directed

and another is undirected. The clustering coefficient of the directed

network is much smaller than the undirected one. The clustering

coefficients of directed and undirected network are both larger than before.

It indicates that the clustering attribute of Chinese Education Network in

the strengthened gradually.

Extracted from the China Education Network data we acquire a new

network named campus network which stands for the connections between

units. The in degree distribution of the campus networks is a power law

distribution with exponential of -0.9. The out degree distribution is a power

law distribution of double section. The first section of the power index is -

1.2 and the second one is -2.1. We calculate the nodes’ k-shell value and its

distribution of this network. We investigate the correlation between node

degree, k-shell value, weighted LeaderRank. Among out degree, in degree,

out k-shell, in k-shell, in degree is the best to indicate the important of a

node. The campus network is a small-word network for the average shortest

path is small and the clustering coefficient is large.

We investigate the effects of the distance between two initial spreaders

for School, Network Facebook and Twitter. There is no significant effect on

School Network. Results from the Facebook and Twitter show that for the

spreaders whose spreading ability is low, the spreading efficiency will

increase when the distance less than a certain value, or decrease otherwise.

However, the spreading will be more effective when the distance between

the two spreaders increase whose spreading ability is high. This work may

give new insights to explore spreading and find better strategy for

spreading.

Key words: Complex network; China Education Network; Topology

structure; spreading effect; distance;

目  录
中文摘要
ABSTRACT
第一章 绪 论........................................................1
1 研究背景及其意义..............................................1
2 国内外研究现状................................................3
3 本文的主要工做................................................4
第二章复杂网络基本理论.............................................5
1 复杂网络拓扑结构属性..........................................5
1.1 度......................................................5
1.2 度分布..................................................6
1.2 平均最短路径.............................................7
1.3 群聚系数.................................................8
1.4K-shell 中心性............................................9
2 复杂网络基本模型.............................................10
2.1 规则网络模型...........................................10
2.2 ER 随机网络模型.........................................11
2.3 小世界网络模型..........................................11
3 复杂网络中经典的传播模型.....................................12
3.1 SI 模型.................................................13
3.2 SIS 模型................................................13
3.3 SIR 模型................................................14
4 传播源间的距离对传播效果的影响...............................14
5 基于随机游走的节点重要性测度.................................15
4.1PageRank 算法............................................16
4.2LeaderRank 算法..........................................16
4.3 加权 LeaderRank 算法.....................................17
6 本章小结.....................................................18
第三章中国教育网拓扑结构特性研究..................................19
1 数据准备和网络构建...........................................19
2 中国教育网节点度分布研究.....................................19
3 中国教育网群聚属性分析.......................................22
4 网络度相关性分析.............................................23

5 本章小结.....................................................24
第四章校园关系网络拓扑结构分析....................................25
1 网络构建.....................................................25
2 校园关系网络拓扑结构特性.....................................25
2.1 校园网节点度分布特性....................................25
2.2 网络的小世界性..........................................26
3 网络节点的 k-shell 中心性以及 k-shell 分布......................26
4 相关性分析...................................................27
4.1 度与 k-shell 的相关性....................................27
4.2 与加权 LeaderRank 值的相关性.............................28
5 本章小结.....................................................30
第五章 传播源间的距离对于传播效果的影响............................31
1 相关理论.....................................................31
1.1 节点之间的距离..........................................31
1.2 变体 SIR 模型............................................31
2 网络描述.....................................................32
4 实验仿真.....................................................33
5 实验结果稳定性分析...........................................37
6 本章小结.....................................................38
第六章 总结与展望..................................................39
1 论文总结.....................................................39
2 展望.........................................................39

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摘要：

摘要互联网的高速发展为人类的生活和工作带来了深远的影响，在很大程度上改变了人们获取信息的方式和交流习惯。Web2.0技术的出现给互联网带来了深刻的变革，由最早的博客到后来出现的贴吧、论坛、微博、Facebook、Twitter等社交工具，为人们的交流带来了极大的方便，人们利用这些工具可以低成本的维持好友关系使信息的传播变得比以往任何时候都要迅速。新技术的出现给互联网用户带来了全新的体验，然而中国教育网作为互联网的重要组成部分，在中国的教育科研事业中起到了举足轻重的作用，新技术对中国教育网的拓扑结构产生了怎样的影响，传播源之间的距离对于复杂网络上信息的传播会产生怎样的影响。针对这两个问题，本文做...

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