Scale-free networks : complex webs in nature and technology / Guido Caldarelli.

Format:

Book

Author/Creator:

Caldarelli, Guido.

Language:

English

Subjects (All):

System analysis.

Physical Description:

xiv, 309 pages : illustrations ; 25 cm

Place of Publication:

Oxford ; New York : Oxford University Press, 2007.

Summary:

A variety of different social, natural and technological systems can be described by the same mathematical framework. This holds from Internet to the Food Webs and to the connections between different company boards given by common directors. In all these situations a graph of the elements and their connections displays a universal feature of some few elements with many connections and many with few. This book reports the experimental evidence of these Scale-free networks'' and provides to students and researchers a corpus of theoretical results and algorithms to analyse and understand these features. The contents of this book and their exposition makes it a clear textbook for the beginners and a reference book for the experts.

Contents:

I Definitions and Methodology

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

2.2 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

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 Barabasi-Albert model 112

5.4 Modifications to the Barabasi-Albert model 114

5.5 Copying models 118

5.6 Fitness based model 119

5.7 Graph from optimization principles 123

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

B Graph quantities 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.

Notes:

Includes bibliographical references and index.

ISBN:

9780199211517

0199211515

OCLC:

77540519