Book 图书名称：Scale-free Networks
Author 作者： Guido Caldarelli
Publisher 出版社：Oxford finance
Page 页数： 300
Publishing Date 出版时间： 2007                  
Language 语言：English
Size 大小： 9.8 MB
Format 格式：pdf


Contents
I DEFINITIONS AND METHODOLOGY
1. Introduction to graphs 7
1.1 Graphs, directed graphs, and weighted graphs 10
1.2 Trees 18
1.3 Vertex correlation, assortativity 23
1.4 Hierarchical properties of graphs 29
1.5 The properties of scale-free networks 30
2. Graph structures: communities 34
2.1 Introduction 34
2.2 Typical subgraphs, motifs 36
2.3 Classes of vertices 38
2.4 Centrality measures, betweenness, and robustness 39
2.5 Clustering detection, modularity 41
2.6 Communities in graphs 43
3. Scale-invariance 60
3.1 Geometrical scale-invariance: fractals 62
3.2 Measuring the fractal dimension 67
3.3 Scale-invariance and power laws 70
3.4 Plotting a power law 71
3.5 Scale-invariance in natural sciences 74
3.6 Scale-invariance in economics and in social sciences 81
4. The origin of power-law functions 84
4.1 Random walk, Laplace equation, and fractals 86
4.2 Power laws from minimization principles 92
4.3 Multiplicative processes and normal distribution 95
viii Contents
4.4 Preferential attachment, the Matthew effect 100
5. Graph generating models 103
5.1 Random graph model 105
5.2 The small-world model 108
5.3 The Barab′asi-Albert model 112
5.4 Modifications to the Barab′asi-Albert model 114
5.5 Copying models 118
5.6 Fitness based model 119
5.7 Graph from optimization principles 123
II EXAMPLES
6. Networks in the cell 131
6.1 Basic cell biology 134
6.2 Protein–protein interaction network 138
6.3 Metabolic pathways 142
6.4 Gene regulatory networks 146
7. Geophysical networks 148
7.1 Satellite images and digital elevation models 150
7.2 Geometrical scale invariance for river networks 152
7.3 Scaling relations for river networks 155
7.4 River networks models 157
7.5 River networks on Mars’ surface 164
8. Ecological networks 167
8.1 Species and evolution 170
8.2 Food webs: a very particular case of network 173
8.3 Food web quantities 174
8.4 Classifications of species 179
8.5 Yule process for taxonomies 180
9. Technological networks: Internet and WWW 185
9.1 The Internet protocols 188
9.2 The geography of the Internet 193
9.3 The autonomous systems 196
9.4 The scale-invariance in the Internet 197
9.5 The World Wide Web 199
9.6 Searching the web 200
9.7 Statistical measures of the Web 205
9.8 E-mail networks 208
10. Social and cognitive networks 211
10.1 Networks of scientific papers 213
10.2 Contact networks 219
10.3 Linguistic networks 224
10.4 Wikipedia 229
11. Financial networks 231
11.1 Board of directors 233
11.2 Stock networks 235
11.3 Bank networks 245
11.4 The world trade web 248
III APPENDICES
A. Glossary 253
B. Graph quantities 256
B.1 Basics 256
B.2 Different kinds of graphs 257
B.3 Paths, cycles, and trees 260
C. Basic statistics 262
C.1 Events and probability 262
C.2 Probability densities and distributions 263
C.3 Working with statistical distributions 267
C.4 Statistical properties of weighted networks 272
D. Matrices and eigenvectors 275
E. Population dynamics 277
E.1 Population dynamics 277