网络数据统计分析：电子书概览

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"《Statistical Analysis of Network Data: Methods and Models》是一本专注于网络数据统计分析的电子书，提供高清版本，更新至最新，并且是经典的IT领域著作，以英文呈现。该书由一系列知名专家顾问指导，如P.Bickel、P.Diggle、S.Fienberg、U.Gather、I.Olkin和S.Zeger等人，归属于Springer的统计学系列，旨在深入探讨网络数据分析的理论与实践方法。" 这本书涵盖多个统计学的重要分支，包括但不限于： 1. **度量理论与概率理论**：如Athreya/Lahiri的著作，对基础数学概念进行了深入解析，为后续复杂的统计分析奠定基础。 2. **多元统计分析**：Bilodeau/Brenner的书籍强调了在多变量环境下如何进行统计推断，这对于处理网络数据中复杂关系的理解至关重要。 3. **时间序列分析与预测**：Brockwell/Davis的作品介绍了时间序列的基本概念和预测技术，网络数据中常常包含时间相关的模式，这在分析动态网络时非常有用。 4. **金融数据的统计分析**：Carmona的书专门针对S-PLUS软件中的金融数据分析，揭示了如何应用统计方法处理金融市场中的网络数据。 5. **独立性、可交换性和鞅**：Chow/Teicher的著作深入讨论了概率论中的这些核心概念，这些在理解网络数据的随机结构中起着关键作用。 6. **线性模型**：Christensen的几部作品详细阐述了线性模型在多变量、时间序列和空间数据中的应用，以及非参数回归和响应面最大化等高级主题。 7. **逻辑回归和log线性模型**：进一步解释了如何在复杂的网络结构中运用这些模型进行分类和关联分析。 8. **重复测量的统计方法**：Davis的书提供了处理网络数据中重复观测的统计工具，这对于研究动态变化的网络尤其有价值。 9. **实验设计与分析**：Dean/Voss的著作涵盖了实验设计的基础知识，这对于网络数据的采样和实验研究具有指导意义。 10. **概率与统计的现代介绍**：Dekking等人合著的书籍为初学者提供了现代统计学的入门指南，有助于构建分析网络数据的理论框架。 11. **随机过程基础**：Durrett的书则关注随机过程的核心概念，对于理解网络数据的随机动态非常有帮助。 12. **图模型**：最后，Edwards的书介绍了图模型，这是一种描述网络结构及其变量间关系的有效工具。通过对这些主题的深入学习，读者将能够掌握处理和分析网络数据的统计方法，理解网络结构中的模式和关系，以及如何利用这些知识来解决实际问题。无论是对学术研究还是业界实践，这本书都提供了一个全面而深入的网络数据分析视角。

4 1 Introduction and Overview

a 100-node research network in the mid-1970s, the Internet today is effectively a

network of networks, linking on the order of hundreds of millions of devices and

responsible for carrying the communication trafﬁc that underlies everything from

electronic banking transactions to email correspondence to music, video, and gam-

ing entertainment.

Figure 1.1 shows a visual representation of a portion of the Internet, at a certain

level of granularity – the sub-network known as Abilene. Abilene is part of the In-

ternet2 project,

a research project devoted to development of the ‘next generation’

Internet. It serves as a so-called ‘backbone’ network for universities and research

labs across the United States in a manner analogous to the federal highway system

of roads. The 11 large-scale ‘Core’ nodes in this network correspond to regional

network aggregation points, connected by systems of optical transportation tech-

nologies and routing devices, denoted here as links. In addition, connected to each

Core node are additional nodes, such as ‘Connector’ nodes and ‘Exchange Points.’

The Connector nodes are network infrastructures through which local ‘Participant’

networks from universities and research labs access Abilene; the Exchange Points

are similar, but instead serve to integrate Abilene with other ‘Peer’ Networks, such

as similar networks in other countries. Note the clear hierarchical structure, which

also continues down into the Participant networks themselves, and is replicated in

the Peer networks, ultimately descending down to the laptops and such sitting in

people’s ofﬁces.

While most people largely take the Internet for granted, as a part of the infras-

tructure around which their daily lives are built, there is substantial interest in mea-

suring and studying the Internet, in both the research and commercial communities.

Network-oriented questions regarding the Internet tend to focus on those relating to

its topology, the trafﬁc it carries, the interaction of the two, and in turn the interac-

tion of those with social and economic factors. For example, in regards to topology

we may ask, “What does the Internet look like?” “How big is it?” and “What are

its structural characteristics?” In terms of trafﬁc, questions include “How much traf-

ﬁc is ﬂowing across the network?” “How can I distinguish between ‘normal’ and

‘anomalous’ trafﬁc?” and “Does my network have the capacity to meet anticipated

demands?” See the book by Crovella and Krishnamurthy [105], for example.

In order to answer questions like these, measurements are taken in the Internet

in a variety of active and passive manners. For example, it is possible to actively

probe the Internet with small packets of trafﬁc and register the responses that return

to the sender as a result of communication protocols, which provides information on

the routes the packets traveled and hence some insight into Internet topology. Con-

versely, it is also possible to ‘sit’ passively on an Internet link and monitor the trafﬁc

ﬂowing by to a greater or lesser extent, depending on the granularity of information

desired. We will see statistical topics of particular relevance to measurements like

these in Chapter 3 (i.e., mapping networks), Chapter 5 (i.e., network sampling bias),

Chapter 7 (i.e., Internet topology identiﬁcation), Chapter 8 (i.e., spread of epidemics

in a network), and Chapter 9 (i.e., analysis of network ﬂow data).

http://www.internet2.edu/

6 1 Introduction and Overview

of other areas, such as business and public health. The focus in these areas typically

is on social structure and the quantitative characterization and analysis of such struc-

ture, which they aim to accomplish through the measurement of social interactions

and the analysis of the resulting social network topologies. Questions of interest

include “Who interacts with whom and what factors inﬂuence the tendency to inter-

act?” “Which interactions are mutual?” “Are friends of friends also friends?” “What

social groups, if any, exist in the network?”, “Who are the power brokers?” “Who is

central to the network and who is peripheral?” and “Which actors are similar in the

roles they play?”

Figure 1.2 shows a visual representation of a particular social network, the so-

called ‘karate club network’ of Zachary [411]. Nodes represent members of a karate

club observed by Zachary for roughly two years during the 1970’s, and links con-

necting two nodes indicate social interactions between the two members (thickness

of the links reﬂects relative frequency of interactions). This dataset is somewhat

unique in that Zachary had the curious fortune (from a scientiﬁc perspective) to wit-

ness the club split into two different clubs during his period of observation, due to a

dispute between the head teacher and an administrator. It was originally published

in conjunction with a model for information ﬂow in small groups in the presence

of conﬂict and ﬁssion. It has since become a favorite among researchers developing

algorithms for detection of social subgroups, since the truth of membership in the

two subgroups is a known quantity.

Social network scientists often face unique measurement challenges. Potential

difﬁculties include the identiﬁcation of social entities of interest, their willingness

to be recruited into studies, and possible sources of bias in their response. For ex-

ample, drug addicts or sex workers, two subpopulations of considerable interest to

those studying the impact of social structure on the spread of the AIDS virus, are

not necessarily obvious to identify in the general population. Once identiﬁed, they

may have serious qualms about participating in a study. And once having agreed,

in principle, to participate, they may be understandably reluctant to fully disclose

information on, say, the sharing of hypodermic needles or their sexual partners. All

of these issues, and others like them, can have an important impact on the statistical

analysis of such data.

In recent years, the Internet has begun to have a fascinating impact on the ﬁeld

of social network analysis, due both to the potential for large-scale data acquisition

and storage and the actual types of social interactions facilitated by the Internet.

Examples of networks whose study is impacted in this manner include networks

of email exchanges or phone calls, which can be measured by exploiting the exist-

ing computer infrastructure in the underlying technological networks, or networks

of scientiﬁc collaborations, now relatively easily compiled on large scales because

of the prevalence of electronic publication and archiving. Many of these networks

are signiﬁcantly larger than the size of typical social networks studied in the past.

However, this characteristic can lead to its own issues. For example, the sheer mag-

nitude of emails sent or calls made daily on a service provider’s network quickly

leads to concerns about data volume, which can make even seemingly simple tasks

of network summary and visualization highly nontrivial.

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