| 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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