Lectures on Complex Networks (Oxford Master Series in Physics)

✍ Scribed by Sergey Dorogovtsev

• Publisher: Oxford University Press
• Year: 2010
• Tongue: English
• Leaves: 145
• Edition: Illustrated
• Category: Library

✦ Synopsis

This text is a concise modern introduction to the science of complex networks, and is based on lectures for university students and non-specialists. The author aims to introduce a reader without serious background in mathematics or physics to the world of networks. The lectures fill the existing gap between popular science books and comprehensive reference volumes on complex networks, and provide the shortest path to the world of networks, discussing the main directions of modern research in this active field, as well as the history of network studies. The text describes the current state of the art in complex networks and includes recent results, and will be useful for both teaching and self-study.

✦ Table of Contents

Lectures on complex networks
OXFORD MASTER SERIES IN PHYSICS
Title Page
Preface
Contents
1 First steps towards networks
1.1 Euler’s graph
1.2 Examples of graphs
1.3 Shortest path leiigth
1.4 Lattices and fractals
1.5 Milgrain’s experiment
1.6 Directed networks
1.7 What are raiidoin networks?
1.8 Degree distribution
1.9 Clustering
1.10 Adjacency matrix
2 Classical random graphs
2.1 Two classical models
2.2 Loops in classical random graphs
2.3 Diameter of classical random graphs
2.4 The birth of a giant component
2.5 Finite components
3 Small and large worlds
3.1 The world of Paul Erd˝os
3.2 Diameter of the Web
3.3 Small-world networks
3.4 Equilibrium versus growing trees
3.5 Giant connected component at birth is fractal
3.6 Dimensionality of a brush
4 From the Internet to cellular nets
4.1 Levels of the Internet
4.2 The WWW
4.3 Cellular networks
4.4 Co-occurrence networks
5 Uncorrelated networks
5.1 The configuration model
5.2 Hidden variables
5.3 Neighbour degree distribution
5.4 Loops in uncorrelated networks
5.5 Statistics of shortest paths
5.6 Uncorrelated bipartite networks
6 Percolation and epidemics
6.1 Connected components in uncorrelated networks
6.2 Ultra-resilience phenomenon
6.3 Finite-size effects
6.4 k-cores
6.5 Epidemics in networks
7 Self-organization of networks
7.1 Random recursive trees
7.2 The Barab´asi–Albert model
7.3 General preferential attachment
7.4 Condensation phenomena
7.5 Accelerated growth
7.6 The BKT transition
7.7 Deterministic graphs
8 Correlations in networks
8.1 Degree–degree correlations
8.2 How to measure correlations
8.3 Assortative and disassortative mixing
8.4 Why are networks correlated?
8.5 Degree correlations and clustering
9 Weighted networks
9.1 The strength of weak ties
9.2 World-wide airport network
9.3 Modelling weighted networks
10 Motifs, cliques, communities
10.1 Cliques in networks
10.2 Statistics of motifs
10.3 Modularity
10.4 Detecting communities
10.5 Hierarchical architectures
11 Navigation and search
11.1 Random walks on networks
11.2 Biased random walks
11.3 Kleinberg’s problem
11.4 Navigability
11.5 Google PageRank
12 Traffic
12.1 Traffic in the Internet
12.2 Congestion
12.3 Cascading failures
13 Interacting systems on networks
13.1 The Ising model on networks
13.2 Critical phenomena
13.3 Synchronization
13.4 Games on networks
13.5 Avalanches as branching processes
14 Optimization
14.1 Critique of preferential attachment
14.2 Optimized trade-offs
14.3 The power of choice
15 Outlook
Further reading
References
Index
@physlib