Chapter
1.3.5 Rich-club phenomenon
2 Networks and complexity
2.1.1 Networks everywhere
2.1.2 Measurements and biases
2.2.1 Small-world yet clustered
2.2.2 Heterogeneity and heavy tails
2.2.3 Higher order statistical properties of networks
2.3 The complicated and the complex
3.1 Randomness and network models
3.1.1 Generalized random graphs
3.1.2 Fitness or “hidden variables” models
3.1.3 The Watts–Strogatz model
3.2 Exponential random graphs
3.3 Evolving networks and the non-equilibrium approach
3.3.1 The preferential attachment class of models
3.3.2 Copy and duplication models
3.3.3 Trade-off and optimization models
3.4 Modeling higher order statistics and other attributes
3.5 Modeling frameworks and model validation
4 Introduction to dynamical processes: theory and simulation
4.1 A microscopic approach to dynamical phenomena
4.2 Equilibrium and non-equilibrium systems
4.3 Approximate solutions of the Master Equation
4.4 Agent-based modeling and numerical simulations
5 Phase transitions on complex networks
5.1 Phase transitions and the Ising model
5.2 Equilibrium statistical physics of critical phenomena
5.2.1 Mean-field theory of phase transitions
5.3 The Ising model in complex networks
5.3.1 Small-world networks
5.3.2 Networks with generic degree distributions
5.4 Dynamics of ordering processes
5.5 Phenomenological theory of phase transitions
6 Resilience and robustness of networks
6.2 Percolation phenomena as critical phase transitions
6.3 Percolation in complex networks
6.4 Damage and resilience in networks
6.5 Targeted attacks on large degree nodes
6.5.1 Alternative ranking strategies
6.6 Damage in real-world networks
7 Synchronization phenomena in networks
7.2 Linearly coupled identical oscillators
7.2.1 Small-world networks
7.2.2 Degree fluctuations: the paradox of heterogeneity
7.2.3 Degree-related asymmetry
7.3 Non-linear coupling: firing and pulse
7.4 Non-identical oscillators: the Kuramoto model
7.4.1 The mean-field Kuramoto model
7.4.2 The Kuramoto model on complex networks
7.5 Synchronization paths in complex networks
7.6 Synchronization phenomena as a topology probing tool
8 Walking and searching on networks
8.1 Diffusion processes and random walks
8.2 Diffusion in directed networks and ranking algorithms
8.3 Searching strategies in complex networks
8.3.2 Search in a small world
8.3.3 Taking advantage of complexity
9 Epidemic spreading in population networks
9.1.1 Compartmental models and the homogeneous assumption
9.1.2 The linear approximation and the epidemic threshold
9.2 Epidemics in heterogeneous networks
9.2.2 The SIR and SIS models
9.2.3 The effect of mixing patterns
9.2.4 Numerical simulations
9.3 The large time limit of epidemic outbreaks
9.3.3 Epidemic models and phase transitions
9.3.4 Finite size and correlations
9.4 Immunization of heterogeneous networks
9.4.1 Uniform immunization
9.4.2 Targeted immunization
9.4.3 Immunization without global knowledge
10 Social networks and collective behavior
10.2 Rumor and information spreading
10.3 Opinion formation and the Voter model
10.6 Coevolution of opinions and network
11 Traffic on complex networks
11.1 Traffic and congestion
11.2 Traffic and congestion in distributed routing
11.2.1 Heterogeneity and routing policies
11.2.2 Adaptive (traffic-aware) routing policies
11.3.2 Avalanches by local failures
11.3.3 Avalanche and routing dynamics
11.3.4 Partial failures and recovery
11.3.5 Reinforcement mechanisms
11.4 Stylized models and real-world infrastructures
12 Networks in biology: from the cell to ecosystems
12.1 Cell biology and networks
12.2 Flux-balance approaches and the metabolic activity
12.3 Boolean networks and gene regulation
12.4 The brain as a network
12.5 Ecosystems and food webs
12.5.1 Dynamics and stability of ecosystems
12.5.2 Coupling topology and dynamics
13 Postface: critically examining complex networks science
Appendix 2 Generating functions formalism
Appendix 3 Percolation in directed networks
A3.1 Purely directed networks
Appendix 4 Laplacian matrix of a graph
Appendix 5 Return probability and spectral density
Dynamical Processes on Complex Networks
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.