
Dynamical Processes on Complex Networks
by Alain Barrat , Marc Barthélemy , Alessandro VespignaniBuy New
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Summary
Author Biography
Table of Contents
Preface | p. xi |
Acknowledgements | p. xv |
List of abbreviations | p. xvii |
Preliminaries: networks and graphs | p. 1 |
What is a network? | p. 1 |
Basic concepts in graph theory | p. 2 |
Statistical characterization of networks | p. 11 |
Weighted networks | p. 19 |
Networks and complexity | p. 24 |
Real-world systems | p. 24 |
Network classes | p. 34 |
The complicated and the complex | p. 47 |
Network models | p. 50 |
Randomness and network models | p. 50 |
Exponential random graphs | p. 58 |
Evolving networks and the non-equilibrium approach | p. 60 |
Modeling higher order statistics and other attributes | p. 72 |
Modeling frameworks and model validation | p. 74 |
Introduction to dynamical processes: theory and simulation | p. 77 |
A microscopic approach to dynamical phenomena | p. 77 |
Equilibrium and non-equilibrium systems | p. 79 |
Approximate solutions of the Master Equation | p. 82 |
Agent-based modeling and numerical simulations | p. 85 |
Phase transitions on complex networks | p. 92 |
Phase transitions and the Ising model | p. 92 |
Equilibrium statistical physics of critical phenomena | p. 96 |
The Ising model in complex networks | p. 101 |
Dynamics of ordering processes | p. 108 |
Phenomenological theory of phase transitions | p. 111 |
Resilience and robustness of networks | p. 116 |
Damaging networks | p. 116 |
Percolation phenomena as critical phase transitions | p. 120 |
Percolation in complex networks | p. 124 |
Damage and resilience in networks | p. 126 |
Targeted attacks on large degree nodes | p. 129 |
Damage in real-world networks | p. 135 |
Synchronization phenomena in networks | p. 136 |
General framework | p. 136 |
Linearly coupled identical oscillators | p. 138 |
Non-linear coupling: firing and pulse | p. 148 |
Non-identical oscillators: the Kuramoto model | p. 151 |
Synchronization paths in complex networks | p. 156 |
Synchronization phenomena as a topology probing tool | p. 158 |
Walking and searching on networks | p. 160 |
Diffusion processes and random walks | p. 160 |
Diffusion in directed networks and ranking algorithms | p. 166 |
Searching strategies in complex networks | p. 170 |
Epidemic spreading in population networks | p. 180 |
Epidemic models | p. 180 |
Epidemics in heterogeneous networks | p. 189 |
The large time limit of epidemic outbreaks | p. 197 |
Immunization of heterogeneous networks | p. 207 |
Complex networks and epidemic forecast | p. 212 |
Social networks and collective behavior | p. 216 |
Social influence | p. 216 |
Rumor and information spreading | p. 218 |
Opinion formation and the Voter model | p. 225 |
The Axelrod model | p. 232 |
Prisoner's dilemma | p. 235 |
Coevolution of opinions and network | p. 238 |
Traffic on complex networks | p. 242 |
Traffic and congestion | p. 242 |
Traffic and congestion in distributed routing | p. 246 |
Avalanches | p. 256 |
Stylized models and real-world infrastructures | p. 264 |
Networks in biology: from the cell to ecosystems | p. 267 |
Cell biology and networks | p. 268 |
Flux-balance approaches and the metabolic activity | p. 271 |
Boolean networks and gene regulation | p. 274 |
The brain as a network | p. 279 |
Ecosystems and food webs | p. 282 |
Future directions | p. 293 |
Postface: critically examining complex networks science | p. 294 |
Random graphs | p. 298 |
Generating functions formalism | p. 303 |
Percolation in directed networks | p. 306 |
Laplacian matrix of a graph | p. 310 |
Return probability and spectral density | p. 311 |
References | p. 313 |
Index | p. 344 |
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