Scale-Free Networks Complex Webs in Nature and Technology

Name: Scale-Free Networks Complex Webs in Nature and Technology | Complex Webs in Nature and Technology
Brand: Oxford University Press
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Complex Webs in Nature and Technology

Caldarelli Guido(Autor*in)

Oxford University Press

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Erschienen am 3. Mai 2007

324 Seiten

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Inhalt

Intro
Contents
I: DEFINITIONS AND METHODOLOGY
1. Introduction to graphs
1.1 Graphs, directed graphs, and weighted graphs
1.2 Trees
1.3 Vertex correlation, assortativity
1.4 Hierarchical properties of graphs
1.5 The properties of scale-free networks
2. Graph structures: communities
2.1 Introduction
2.2 Typical subgraphs, motifs
2.3 Classes of vertices
2.4 Centrality measures, betweenness, and robustness
2.5 Clustering detection, modularity
2.6 Communities in graphs
3. Scale-invariance
3.1 Geometrical scale-invariance: fractals
3.2 Measuring the fractal dimension
3.3 Scale-invariance and power laws
3.4 Plotting a power law
3.5 Scale-invariance in natural sciences
3.6 Scale-invariance in economics and in social sciences
4. The origin of power-law functions
4.1 Random walk, Laplace equation, and fractals
4.2 Power laws from minimization principles
4.3 Multiplicative processes and normal distribution
4.4 Preferential attachment, the Matthew effect
5. Graph generating models
5.1 Random graph model
5.2 The small-world model
5.3 The Barabási-Albert model
5.4 Modifications to the Barabási-Albert model
5.5 Copying models
5.6 Fitness based model
5.7 Graph from optimization principles
II: EXAMPLES
6. Networks in the cell
6.1 Basic cell biology
6.2 Protein-protein interaction network
6.3 Metabolic pathways
6.4 Gene regulatory networks
7. Geophysical networks
7.1 Satellite images and digital elevation models
7.2 Geometrical scale invariance for river networks
7.3 Scaling relations for river networks
7.4 River networks models
7.5 River networks on Mars' surface
8. Ecological networks
8.1 Species and evolution
8.2 Food webs: a very particular case of network
8.3 Food web quantities
8.4 Classifications of species
8.5 Yule process for taxonomies
9. Technological networks: Internet and WWW
9.1 The Internet protocols
9.2 The geography of the Internet
9.3 The autonomous systems
9.4 The scale-invariance in the Internet
9.5 The World Wide Web
9.6 Searching the web
9.7 Statistical measures of the Web
9.8 E-mail networks
10. Social and cognitive networks
10.1 Networks of scientific papers
10.2 Contact networks
10.3 Linguistic networks
10.4 Wikipedia
11. Financial networks
11.1 Board of directors
11.2 Stock networks
11.3 Bank networks
11.4 The world trade web
III: APPENDICES
A. Glossary
A
B
C
D
E
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G
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B. Graph quantities
B.1 Basics
B.2 Different kinds of graphs
B.3 Paths, cycles, and trees
C. Basic statistics
C.1 Events and probability
C.2 Probability densities and distributions
C.3 Working with statistical distributions
C.4 Statistical properties of weighted networks
D. Matrices and eigenvectors
E. Population dynamics
E.1 Population dynamics
Bibliography
Index
A
B
C
D
E
F
G
H
I
K
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