网络科学导论：从技术到社会的网络分析

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"《网络介绍》是一本深入探讨网络理论的英文著作，涵盖了技术网络、社会网络、信息网络、生物网络等多个领域的网络概念。作者M.E.J.Newman在书中介绍了网络数学基础、度量标准、大规模结构、算法基础以及网络模型等方面的知识。此书由牛津大学出版社出版，旨在推进研究、学术和教育的卓越发展，全球多地发行。" 本书首先从"Introduction"开始，引入了网络的基本概念和重要性，为后续章节奠定了基础。"Technological Networks"这部分讨论了如互联网、电信网络等技术基础设施的网络特性。"Social Networks"则关注人类社会中的关系网络，如社交媒体和人际关系网络的形成和演化。 "Information Networks"探讨了信息传播的网络结构，包括搜索引擎、新闻网络和知识图谱。"Biological Networks"深入生物学领域，研究基因调控网络、神经网络等生命系统的网络模型。"Mathematics of Networks"是理论核心，介绍网络的数学理论，如图论和矩阵分析。 "Measures and Metrics"章节详细阐述了度量网络特性的指标，如节点度、聚类系数、平均路径长度等。"The Large-scale Structure of Networks"探讨了网络的大规模结构，如小世界网络和无标度网络的特征。"Basic Concepts of Algorithms"和"Fundamental Network Algorithms"讲解了网络分析中常用的数据处理和算法，如最短路径算法、网络流算法等。 "Matrix Algorithms and Graph Partitioning"关注矩阵方法在图划分问题上的应用，这对于优化网络性能和理解网络结构至关重要。"Random Graphs"和"Generalized Random Graphs"介绍了随机网络模型及其扩展，这些模型在模拟真实网络行为时具有重要意义。"Models of Network Formation"和"Other Network Models"探讨了网络形成的机制和各种网络模型，如偏好附着模型、复合过程模型等。 "Percolation and Network Resilience"研究了网络中的渗流现象和网络韧性，这对于理解网络在受到攻击或故障时的行为至关重要。"Epidemics on Networks"关注传染病在网络中的传播，这对于公共卫生和疾病控制有实际应用价值。"Dynamical Systems on Networks"探讨网络上动态系统的行为，如同步、振荡和分岔现象。 "Network Search"章节关注如何在网络中有效地寻找信息或目标节点。最后，参考文献和索引提供了进一步学习和研究的资源。这本书对于理解复杂网络的结构、动态和应用具有深远的指导意义，适合网络科学、计算社会科学、生物学、信息科学等领域的学者和学生阅读。

Figure 1.3: The food web of Little Rock Lake, Wisconsin. (See Plate II for color version.) This

elegant picture summarizes the known predatory interactions between species in a freshwater lake

in the northern United States. The vertices represent the species and the edges run between

predator-prey species pairs. The vertical position of the vertices represents, roughly speaking, the

trophic level of the corresponding species. The figure was created by Richard Williams and Neo

Martinez [209].

Biochemical networks are discussed in detail in Section 5.1.

Another class of biological networks is that of biochemical networks, such as metabolic

networks, protein-protein interaction networks, and genetic regulatory networks. A metabolic

network, for instance, is a representation of the chemical reactions that fuel cells and organisms.

The reader may have seen the wallcharts of metabolic reactions that adorn the offices of some

biochemists, incredibly detailed maps with hundreds of tiny inscriptions linked by a maze of

arrows.

The inscriptions—the vertices in this network—are metabolites, the substrates and

products of metabolism, and the arrows—directed edges—are reactions that turn one metabolite

into another. The depiction of reactions as a network is one of the first steps towards making sense

of the bewildering array of biochemical data generated by recent and ongoing experiments in

molecular genetics.

These are just a few examples of the types of network whose study is the focus of this book.

There are many others that we will come across in later pages. Among them some of the best

known are telephone networks, road, rail, and air networks, the power grid, citation networks,

recommender networks, peer-to-peer networks, email networks, collaboration networks, disease

transmission networks, river networks, and word networks.

PROPERTIES OF NETWORKS

We have seen that a variety of systems can be represented as networks. If we can gather data on

the structure of one of these networks, what then can we do with those data? What can they tell us

about the form and function of the system the network represents? What properties of networked

systems can we measure or model and how are those properties related to the practical issues we

care about? This, essentially, is the topic of this entire book, and we are not going to answer it in

this chapter alone. Let us, however, look briefly here at a few representative concepts, to get a feel

for the kinds of ideas we will be dealing with.

A first step in analyzing the structure of a network is often to make a picture of it. Figures 1.1,

1.2, and 1.3 are typical examples. Each of these was generated by a specialized computer program

designed for network visualization and there are many such programs available, both commercially

and for free, if you want to produce pictures like these for yourself. Visualization can be an

extraordinarily useful tool in the analysis of network data, allowing one to see instantly important

structural features of a network that would otherwise be difficult to pick out of the raw data. The

human eye is enormously gifted at picking out patterns, and visualizations allow us to put this gift

to work on our network problems. On the other hand, direct visualization of networks is only really

useful for networks up to a few hundreds or thousands of vertices, and for networks that are

relatively sparse, meaning that the number of edges is quite small. If there are too many vertices or

edges in a network then pictures of the network will be too complicated for the eye to comprehend

and their usefulness becomes limited. Many of the networks that scientists are interested in today

have hundreds of thousands or even millions of vertices, which means that visualization is not of

much help in their analysis and we need to employ other techniques to determine their structural

features. In response to this need, network theory has developed a large toolchest of measures and

metrics that can help us understand what our network data are telling us, even in cases where

useful visualization is impossible.

An example of an important and useful class of network measures is that of measures of

centrality. Centrality quantifies how important vertices (or edges) are in a networked system, and

social network analysts in particular have expended considerable effort studying it. There are a

wide variety of mathematical measures of vertex centrality that focus on different concepts and

definitions of what it means to be central in a network. A simple but very useful example is the

measure called degree. The degree of a vertex in a network is the number of edges attached to it. In

a social network of friendships between individuals, for instance, such as the network of Fig. 1.2,

the degree of an individual is the number of friends he or she has within the network. In the

Internet degree would be the number of data connections a computer, router, or other device has.

In many cases the vertices with the highest degrees in a network, those with the most connections,

also play important roles in the functioning of the system, and hence degree can be a useful guide

for focusing our attention on the system’s most crucial elements.

See Chapter 7 for further discussion of centrality measures.

The number beside each vertex in this small network indicates the vertex’s degree.

In undirected networks degree is just a single number, but in directed networks vertices have

two different degrees, in-degree and out-degree, corresponding to the number of edges pointing

inward to and outward from those vertices. For example, the in-degree of a web page is the

number of other pages that link to it and the out-degree is the number of pages to which it links.

We have already mentioned one example of how centrality can be put to use on the Web to answer

an important practical question: by counting the number of links a web page gets—the in-degree of

the page—we (or a search engine operating on our behalf) can make a guess about which pages are

most likely to contain information that might be of use to us.

It is an interesting observation that many networks are found to contain a small but significant

number of “hubs”—vertices with unusually high degree. Social networks often contain a few

central individuals with very many acquaintances; there are a few websites with an extraordinarily

large number of links; there are a few metabolites that take part in almost all metabolic processes.

A major topic of research in recent years has been the investigation of the effects of hubs on the

performance and behavior of networked systems. Both empirical and theoretical results indicate

that hubs can have a quite disproportionate effect, playing a central role particularly in network

transport phenomena and resilience, despite being few in number.

Hubs are discussed further in Section 8.3.

Another example of a network concept that arises repeatedly and has real practical implications

is the so-called small-world effect. One can define a distance, called the geodesic distance,

between two vertices in a network to be the minimum number of edges one would have to traverse

in order to get from one vertex to the other. For instance, two friends would have geodesic distance

1 in a friendship network because there is a single edge connecting them directly, while the friend

of your friend would have distance 2 from you. As discussed in Sections 3.6 and 8.2, it is found

empirically (and can be proven mathematically in some cases) that the mean geodesic distance,

appropriately defined,

between vertex pairs is very short, typically increasing only as the

logarithm of the number of vertices in the network. Although first studied in the context of

friendship networks, this small-world effect appears to be very widespread, occurring in essentially

all types of networks. In popular culture it is referred to as the “six degrees of separation,” after a

successful stage play and film of the same name. The semi-mythological claim is that you can get

from anyone in the world to anyone else via a sequence of no more than five intermediate

acquaintances—six steps in all.

The small-world effect can have interesting repercussions. For example, news and gossip spread

over social networks. If you hear an interesting rumor from a friend, you may pass it on to your

other friends, and they in turn pass it on to theirs, and so forth. Clearly the rumor will spread

further and faster if it only takes six steps to reach anyone in the world than if it takes a hundred, or

a million. It is a matter of common experience that indeed a suitably scandalous rumor can reach

the ears of an entire community in what seems like the blink of an eye, and the structure of social

networks has a lot to do with it.

And consider the Internet. One of the reasons the Internet functions at all is because any

computer on the network is only a few “hops” over optical and other data lines from any other. In

practice the paths taken by packets over the Internet are typically in the range of about ten to

twenty hops long. Certainly the performance of the network would be much worse if packets had

to make a thousand hops instead.

A third example of a network concept of practical importance is provided by clusters or

communities in networks. We are most of us familiar with the idea that social networks break up

into subcommunities—tightly knit groups of friends or acquaintances within the larger, looser

network. Friendship networks, for instance, tend to contain cliques, circles, and gangs of friends

within which connections are strong and frequent but between which they are weaker or rarer. The

OUTLINE OF THIS BOOK

This book is divided into five parts. In the first part, consisting of Chapters 2 to 5, we introduce the

various types of network encountered in the real world, including technological, social, and

biological networks, and the empirical techniques used to discover their structure. Although it is

not the purpose of this book to describe any one particular network in great detail, the study of

networks is nonetheless firmly founded on empirical observations and a good understanding of

what data are available and how they are obtained is immensely helpful in understanding the

science of networks as it is practiced today.

The second part of the book, Chapters 6 to 8, introduces the fundamental theoretical ideas on

which our current understanding of networks is based. Chapter 6 describes the basic mathematics

used to capture network ideas, Chapter 7 describes the measures and metrics we use to quantify

network structure, and Chapter 8 describes some of the intriguing patterns and principles that

emerge when we apply our mathematics and our metrics to real-world network data.

In the third part of the book, Chapters 9 to 11, we discuss computer algorithms for analyzing

and understanding network data. Measurements of network properties, such as those described in

Chapter 7, are typically only possible with the help of fast computers and much effort has been

devoted over the years to the development of efficient algorithms for analyzing network data. This

part of the book describes in detail some of the most important of these algorithms. A knowledge

of this material will be of use to anyone who wants to work with network data.

In the fourth part of the book, Chapters 12 to 15, we look at mathematical models of networks.

The material in these chapters forms a central part of the canon of the field and has been the

subject of a vast amount of published scientific research. We study both traditional models, such as

random graphs and their extensions, and newer models, such as models of growing networks and

the “small-world model.”

Finally, in the fifth and last part of the book, Chapters 16 to 19, we look at processes taking

place on networks, including failure processes and resilience, network epidemiology, dynamical

systems, and network search processes. The theory of these processes is less well developed than

other aspects of the theory of networks and there is much work still to be done. The last chapters of

the book probably raise at least as many questions as they answer, but this, surely, is a good thing.

With luck readers will feel inspired to answer some of those questions themselves and the author

looks forward to the new and excitin

results the

enerate when the

do.

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