Dynamical Processes on Complex Networks

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Edition: 1st
Format: Hardcover
Pub. Date: 2008-11-24
Publisher(s): Cambridge University Press
List Price: $111.00

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Summary

The availability of large data sets has allowed researchers to uncover complex properties such as large scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics, to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-experts in the subject.

Author Biography

Alessandro Vespignani is Professor of Informatics and Adjunct Professor of Physics and Statistics at Indiana University, USA, and Director of the Complex Networks Lagrange Laboratory at the Institute for Scientific Interchange in Turin, Italy.

Table of Contents

Prefacep. xi
Acknowledgementsp. xv
List of abbreviationsp. xvii
Preliminaries: networks and graphsp. 1
What is a network?p. 1
Basic concepts in graph theoryp. 2
Statistical characterization of networksp. 11
Weighted networksp. 19
Networks and complexityp. 24
Real-world systemsp. 24
Network classesp. 34
The complicated and the complexp. 47
Network modelsp. 50
Randomness and network modelsp. 50
Exponential random graphsp. 58
Evolving networks and the non-equilibrium approachp. 60
Modeling higher order statistics and other attributesp. 72
Modeling frameworks and model validationp. 74
Introduction to dynamical processes: theory and simulationp. 77
A microscopic approach to dynamical phenomenap. 77
Equilibrium and non-equilibrium systemsp. 79
Approximate solutions of the Master Equationp. 82
Agent-based modeling and numerical simulationsp. 85
Phase transitions on complex networksp. 92
Phase transitions and the Ising modelp. 92
Equilibrium statistical physics of critical phenomenap. 96
The Ising model in complex networksp. 101
Dynamics of ordering processesp. 108
Phenomenological theory of phase transitionsp. 111
Resilience and robustness of networksp. 116
Damaging networksp. 116
Percolation phenomena as critical phase transitionsp. 120
Percolation in complex networksp. 124
Damage and resilience in networksp. 126
Targeted attacks on large degree nodesp. 129
Damage in real-world networksp. 135
Synchronization phenomena in networksp. 136
General frameworkp. 136
Linearly coupled identical oscillatorsp. 138
Non-linear coupling: firing and pulsep. 148
Non-identical oscillators: the Kuramoto modelp. 151
Synchronization paths in complex networksp. 156
Synchronization phenomena as a topology probing toolp. 158
Walking and searching on networksp. 160
Diffusion processes and random walksp. 160
Diffusion in directed networks and ranking algorithmsp. 166
Searching strategies in complex networksp. 170
Epidemic spreading in population networksp. 180
Epidemic modelsp. 180
Epidemics in heterogeneous networksp. 189
The large time limit of epidemic outbreaksp. 197
Immunization of heterogeneous networksp. 207
Complex networks and epidemic forecastp. 212
Social networks and collective behaviorp. 216
Social influencep. 216
Rumor and information spreadingp. 218
Opinion formation and the Voter modelp. 225
The Axelrod modelp. 232
Prisoner's dilemmap. 235
Coevolution of opinions and networkp. 238
Traffic on complex networksp. 242
Traffic and congestionp. 242
Traffic and congestion in distributed routingp. 246
Avalanchesp. 256
Stylized models and real-world infrastructuresp. 264
Networks in biology: from the cell to ecosystemsp. 267
Cell biology and networksp. 268
Flux-balance approaches and the metabolic activityp. 271
Boolean networks and gene regulationp. 274
The brain as a networkp. 279
Ecosystems and food websp. 282
Future directionsp. 293
Postface: critically examining complex networks sciencep. 294
Random graphsp. 298
Generating functions formalismp. 303
Percolation in directed networksp. 306
Laplacian matrix of a graphp. 310
Return probability and spectral densityp. 311
Referencesp. 313
Indexp. 344
Table of Contents provided by Ingram. All Rights Reserved.

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