没有合适的资源?快使用搜索试试~ 我知道了~
首页《复杂网络:原理、方法与应用》详解:构筑多领域理解的关键
《复杂网络:原理、方法与应用》详解:构筑多领域理解的关键
需积分: 9 30 下载量 106 浏览量
更新于2024-07-17
收藏 23.31MB PDF 举报
《复杂网络大家名著:复杂网络——原理、方法与应用》是一本深度探讨复杂系统核心要素的权威教材。它涵盖了从大脑神经网络到计算机通信,再到交通运输基础设施、在线社交网络,乃至代谢反应和金融市场等各种领域的网络结构研究。这本书旨在通过严谨而全面的教学,让学生深入理解网络科学的新理论和方法。 书中详尽地介绍了各种算法,如图探索算法、节点排名算法和网络生成算法,这些是理解和分析网络数据的基础工具。学生可以借此机会实践网络模型,并运用真实的案例和数据集,从而对网络理论的基本概念有深入的掌握,同时学习其在实际问题中的应用技巧。作者特别关注系统复杂性的增长,通过深入剖析,挑战读者提升他们的技能水平。 作者Vito Latora以其生动的方式呈现了网络科学的重要原则,使得本书不仅适合物理学、数学、工程学等专业背景的研究人员,也适合本科生和研究生,特别是那些在生物学、神经科学和社会科学领域寻找复杂系统答案的学生。无论是在理论研究还是在解决实际问题时,这都是一本不可或缺的参考书,帮助读者更好地洞察和处理现实世界中的网络现象和规律。通过学习这本书,读者将建立起扎实的复杂网络知识体系,为进一步探索复杂系统的奥秘奠定坚实基础。
资源详情
资源推荐
xvi Introduction
Table 1 A list of the real-world complex networks that will be studied in this book. For each network, we
report the chapter of the book where the corresponding data set will be introduced and analysed.
Complex networks Nodes Links Chapter
Elisa’s kindergarten Children Friendships 1
Actor collaboration networks Movie actors Co-acting in a film 2
Co-authorship networks Scientists Co-authoring a paper 3
Citation networks Scientific papers Citations 6
Zachary’s karate club Club members Friendships 9
C. elegans neural network Neurons Synapses 4
Transcription regulation networks Genes Transcription regulation 8
World Wide Web Web pages Hyperlinks 5
Internet Routers Optical fibre cables 7
Urban street networks Street crossings Streets 8
Air transport network Airports Flights 10
Financial markets Stocks Time correlations 10
Both works were motivated by the empirical analysis of real-world systems. Four net-
works were introduced and studied in these two papers. Namely, the neural system of
a few-millimetres-long worm known as the C. elegans , a social network describing how
actors collaborate in movies, and two man-made networks: the US electrical power grid and
a sample of the World Wide Web. During the last decade, new technologies and increasing
computing power have made new data available and stimulated the exploration of several
other complex networks from the real world. A long series of papers has followed, with
the analysis of new and ever larger networks, and the introduction of novel measures and
models to characterise and reproduce the structure of these real-world systems. Table 1
shows only a small sample of the networks that have appeared in the literature, namely
those that will be explicitly studied in this book, together with the chapter where they
will be considered. Notice that the table includes different types of networks. Namely,
five networks representing three different types of social interactions (namely friendships,
collaborations and citations), two biological systems (respectively a neural and a gene net-
work) and five man-made networks (from transportation and communication systems to a
network of correlations among financial stocks).
The ubiquitousness of networks in nature, technology and society has been the principal
motivation behind the systematic quantitative study of their structure, their formation and
their evolution. And this is also the main reason why a student of any scientific discipline
should be interested in complex networks. In fact, if we want to master the interconnected
world we live in, we need to understand the structure of the networks around us. We have
to learn the basic principles governing the architecture of networks from different fields,
and study how to model their growth.
It is also important to mention the high interdisciplinarity of network science. Today,
research on complex networks involves scientists with expertise in areas such as mathe-
matics, physics, computer science, biology, neuroscience and social science, often working
.002
22:17:26, subject to the Cambridge Core terms of use,
xvii Introduction
1995
2000
2005
2010
2015
year
0
2000
4000
6000
8000
10000
# citations
WS
BA
1995
2000
2005
2010
2015
y
ear
200
400
600
800
# papers
t
Fig. 1
Left panel: number of citations received over the years by the 1998 Watts and Strogatz (WS) article on small-world
networks and by the 1999 Barabási and Albert (BA) article on scale-free networks. Right panel: number of papers on
complex networks that appeared each year in the public preprint archive arXiv.org.
side by side. Because of its interdisciplinary nature, the generality of the results obtained,
and the wide variety of possible applications, network science is considered today a
necessary ingredient in the background of any modern scientist.
Finally, it is not difficult to understand that complex networks have become one of the
hottest research fields in science. This is confirmed by the attention and the huge number
of citations received by Watts and Strogatz, and by Barabási and Albert, in the papers
mentioned above. The temporal profiles reported in the left panel of Figure 1 show the
exponential increase in the number of citations of these two papers since their publication.
The two papers have today about 10,000 citations each and, as already mentioned, have
opened a new research field stimulating interest for complex networks in the scientific
community and triggering an avalanche of scientific publications on related topics. The
right panel of Figure 1 reports the number of papers published each year after 1998 on the
well-known public preprint archive arXiv.org with the term “complex networks” in their
title or abstract. Notice that this number has gone up by a factor of 10 in the last ten years,
with almost a thousand papers on the topic published in the archive in the year 2013. The
explosion of interest in complex networks is not limited to the scientific community, but
has become a cultural phenomenon with the publications of various popular science books
on the subject.
Overview of the Book
This book is mainly intended as a textbook for an introductory course on complex networks
for students in physics, mathematics, engineering and computer science, and for the more
mathematically oriented students in biology and social sciences. The main purpose of the
book is to expose the readers to the fundamental ideas of network science, and to provide
them with the basic tools necessary to start exploring the world of complex networks. We
also hope that the book will be able to transmit to the reader our passion for this stimulating
new interdisciplinary subject.
.002
22:17:26, subject to the Cambridge Core terms of use,
xviii Introduction
The standard tools to study complex networks are a mixture of mathematical and com-
putational methods. They require some basic knowledge of graph theory, probability,
differential equations, data structures and algorithms, which will be introduced in this
book from scratch and in a friendly way. Also, network theory has found many interest-
ing applications in several different fields, including social sciences, biology, neuroscience
and technology. In the book we have therefore included a large variety of examples to
emphasise the power of network science. This book is essentially on the structure of com-
plex networks, since we have decided that the detailed treatment of the different types of
dynamical processes that can take place over a complex network should be left to another
book, which will follow this one.
The book is organised into ten chapters. The first six chapters (Chapters 1–6) form the
core of the book. They introduce the main concepts of network science and the basic
measures and models used to characterise and reproduce the structure of various com-
plex networks. The remaining four chapters (Chapters 7–10) cover more advanced topics
that could be skipped by a lecturer who wants to teach a short course based on the book.
In Chapter 1 we introduce some basic definitions from graph theory, setting up the lan-
guage we will need for the remainder of the book. The aim of the chapter is to show
that complex network theory is deeply grounded in a much older mathematical discipline,
namely graph theory.
In Chapter 2 we focus on the concept of centrality, along with some of the related mea-
sures originally introduced in the context of social network analysis, which are today used
extensively in the identification of the key components of any complex system, not only
of social networks. We will see some of the measures at work, using them to quantify the
centrality of movie actors in the actor collaboration network.
Chapter 3 is where we first discuss network models. In this chapter we introduce the
classical random graph models proposed by Erd
˝
os and Rényi (ER) in the late 1950s, in
which the edges are randomly distributed among the nodes with a uniform probability.
This allows us to analytically derive some important properties such as, for instance, the
number and order of graph components in a random graph, and to use ER models as term
of comparison to investigate scientific collaboration networks. We will also show that the
average distance between two nodes in ER random graphs increases only logarithmically
with the number of nodes.
In Chapter 4 we see that in real-world systems, such as the neural network of the C. ele-
gans or the movie actor collaboration network, the neighbours of a randomly chosen node
are directly linked to each other much more frequently than would occur in a purely ran-
dom network, giving rise to the presence of many triangles. In order to quantify this, we
introduce the so-called clustering coefficient. We then discuss the Watts and Strogatz (WS)
small-world model to construct networks with both a small average distance between nodes
and a high clustering coefficient.
In Chapter 5 the focus is on how the degree k is distributed among the nodes of a network.
We start by considering the graph of the World Wide Web and by showing that it is a
scale-free network, i.e. it has a power–law degree distribution p
k
∼ k
−γ
with an exponent
γ ∈ [2, 3]. This is a property shared by many other networks, while neither ER random
graphs nor the WS model can reproduce such a feature. Hence, we introduce the so-called
.002
22:17:26, subject to the Cambridge Core terms of use,
xix Introduction
configuration model which generalises ER random graph models to incorporate arbitrary
degree distributions.
In Chapter 6 we show that real networks are not static, but grow over time with the
addition of new nodes and links. We illustrate this by studying the basic mechanisms of
growth in citation networks. We then consider whether it is possible to produce scale-free
degree distributions by modelling the dynamical evolution of the network. For this purpose
we introduce the Barabási–Albert model, in which newly arriving nodes select and link
existing nodes with a probability linearly proportional to their degree. We also consider
some extensions and modifications of this model.
In the last four chapters we cover more advanced topics on the structure of complex
networks.
Chapter 7 is about networks with degree–degree correlations, i.e. networks such that the
probability that an edge departing from a node of degree k arrives at a node of degree k
is a function both of k
and of k. Degree–degree correlations are i ndeed present in real-
world networks, such as the Internet, and can be either positive (assortative) or negative
(disassortative). In the first case, networks with small degree preferentially link to other
low-degree nodes, while in the second case they link preferentially to high-degree ones. In
this chapter we will learn how to take degree–degree correlations into account, and how to
model correlated networks.
In Chapter 8 we deal with the cycles and other small subgraphs known as motifs which
occur in most networks more frequently than they would in random graphs. We consider
two applications: firstly we count the number of short cycles in urban street networks of
different cities from all over the world; secondly we will perform a motif analysis of the
transcription network of the bacterium E. coli.
Chapter 9 is about network mesoscale structures known as community structures.Com-
munities are groups of nodes that are more tightly connected to each other than to other
nodes. In this chapter we will discuss various methods to find meaningful divisions of
the nodes of a network into communities. As a benchmark we will use a real network, the
Zachary’s karate club, where communities are known a priori, and also models to construct
networks with a tunable presence of communities.
In Chapter 10 we deal with weighted networks, where each link carries a numerical value
quantifying the intensity of the connection. We will introduce the basic measures used to
characterise and classify weighted networks, and we will discuss some of the models of
weighted networks that reproduce empirically observed topology–weight correlations. We
will study in detail two weighted networks, namely the US air transport network and a
network of financial stocks.
Finally, the book’s Appendix contains a detailed description of all the main graph algo-
rithms discussed in the various chapters of the book, from those to find shortest paths,
components or community structures in a graph, to those to generate random graphs or
scale-free networks. All the algorithms are presented in a
C-like pseudocode format which
allows us to understand their basic structure without the unnecessary complication of a
programming language.
The organisation of this textbook is another reason why it is different from all the other
existing books on networks. We have in fact avoided the widely adopted separation of
.002
22:17:26, subject to the Cambridge Core terms of use,
xx Introduction
the material in theory and applications, or the division of the book into separate chap-
ters respectively dealing with empirical studies of real-world networks, network measures,
models, processes and computer algorithms. Each chapter in our book discusses, at the
same time, real-world networks, measures, models and algorithms while, as said before,
we have left the study of processes on networks to an entire book, which will follow this
one. Each chapter of this book presents a new idea or network property: it introduces a
network data set, proposes a set of mathematical quantities to investigate such a network,
describes a series of network models to reproduce the observed properties, and also points
to the related algorithms. In this way, the presentation follows the same path of the current
research in the field, and we hope that it will result in a more logical and more entertaining
text. Although the main focus of this book is on the mathematical modelling of complex
networks, we also wanted the reader to have direct access to both the most famous data
sets of real-world networks and to the numerical algorithms to compute network proper-
ties and to construct networks. For this reason, the data sets of all the real-world networks
listed in Table 1 are introduced and illustrated in special DATA SET Boxes, usually one
for each chapter of the book, and can be downloaded from the book’s webpage at
www.
complex-networks.net
. On the same webpage the reader can also find an implemen-
tation in the
C language of the graph algorithms illustrated in the Appendix (in C-like
pseudocode format). We are sure that the student will enjoy experimenting directly on real-
world networks, and will benefit from the possibility of reproducing all of the numerical
results presented throughout the book.
The style of the book is informal and the ideas are illustrated with examples and appli-
cations drawn from the recent research literature and from different disciplines. Of course,
the problem with such examples is that no-one can simultaneously be an expert in social
sciences, biology and computer science, so in each of these cases we will set up the relative
background from scratch. We hope that it will be instructive, and also fun, to see the con-
nections between different fields. Finally, all the mathematics is thoroughly explained, and
we have decided never to hide the details, difficulties and sometimes also the incoherences
of a science still in its infancy.
Acknowledgements
Writing this book has been a long process which started almost ten years ago. The book has
grown from t he notes of various university courses, first taught at the Physics Department
of the University of Catania and at the Scuola Superiore di Catania in Italy, and more
recently to the students of the Masters in “Network Science” at Queen Mary University of
London.
The book would not have been the same without the interactions with the students we
have met at the different stages of the writing process, and their scientific curiosity. Special
thanks go to Alessio Cardillo, Roberta Sinatra, Salvatore Scellato and the other students
and alumni of Scuola Superiore, Salvatore Assenza, Leonardo Bellocchi, Filippo Caruso,
Paolo Crucitti, Manlio De Domenico, Beniamino Guerra, Ivano Lodato, Sandro Meloni,
.002
22:17:26, subject to the Cambridge Core terms of use,
剩余574页未读,继续阅读
weixin_42212193
- 粉丝: 2
- 资源: 26
上传资源 快速赚钱
- 我的内容管理 展开
- 我的资源 快来上传第一个资源
- 我的收益 登录查看自己的收益
- 我的积分 登录查看自己的积分
- 我的C币 登录后查看C币余额
- 我的收藏
- 我的下载
- 下载帮助
最新资源
- 新型矿用本安直流稳压电源设计:双重保护电路
- 煤矿掘进工作面安全因素研究:结构方程模型
- 利用同位素位移探测原子内部新型力
- 钻锚机钻臂动力学仿真分析与优化
- 钻孔成像技术在巷道松动圈检测与支护设计中的应用
- 极化与非极化ep碰撞中J/ψ的Sivers与cos2φ效应:理论分析与COMPASS验证
- 新疆矿区1200m深孔钻探关键技术与实践
- 建筑行业事故预防:综合动态事故致因理论的应用
- 北斗卫星监测系统在电网塔形实时监控中的应用
- 煤层气羽状水平井数值模拟:交替隐式算法的应用
- 开放字符串T对偶与双空间坐标变换
- 煤矿瓦斯抽采半径测定新方法——瓦斯储量法
- 大倾角大采高工作面设备稳定与安全控制关键技术
- 超标违规背景下的热波动影响分析
- 中国煤矿选煤设计进展与挑战:历史、现状与未来发展
- 反演技术与RBF神经网络在移动机器人控制中的应用
资源上传下载、课程学习等过程中有任何疑问或建议,欢迎提出宝贵意见哦~我们会及时处理!
点击此处反馈
安全验证
文档复制为VIP权益,开通VIP直接复制
信息提交成功