Table of Contents

Part I: Single and multilayer networks
1. Complex systems as multilayer networks
Part II: Single networks
2. The structure of single networks
3. The dynamics on single networks
Part III: Multilayer networks
4. Multilayer networks in nature, society and infrastructures
5. The mathematical definition
6. Basic structural properties
7. Structural correlations of multiplex networks
8. Communities
9. Centrality measures
10. Multilayer network models
11. Interdependent multilayer networks
12. Classical percolation, generalized percolation and cascades
13. Epidemic spreading
14. Diffusion
15. Synchronization, non-linear dynamics and control
16. Opinion dynamics and game theory
Appendix A. The Barabasi Albert model: the master equation
Appendix B. Entropy and null models of single networks
Appendix C. Growing multiplex networks: the master equation
Appendix D. Percolation of interdependent networks
Appendix E. Directed percolation of interdependent networks
Appendix F. Immunization strategies on multiplex networks
Appendix G. Spectrum of the Supra-Laplacian
Part I: Single and multilayer networks
1. Complex systems as multilayer networks
Part II: Single networks
2. The structure of single networks
3. The dynamics on single networks
Part III: Multilayer networks
4. Multilayer networks in nature, society and infrastuctures
5. The mathematical definition
6. Basic structural properties
7. Structural correlations of multiplex networks
8. Communities
9. Centrality measures
10. Multilayer network models
11. Interdependent multilayer networks
12. Classical percolation, generalized percolation and cascades
13. Epidemic spreading
14. Diffusion
15. Synchronization, non-linear dynamics and control
16. Opinion dynamics and game theory
Appendix A. The Barabasi Albert model: the master equation
Appendix B. Entropy and null models of single networks
Appendix C. Growing multiplex networks: the master equation
Appendix D. Percolation of interdependent networks
Appendix E. Directed percolation of interdependent networks
Appendix F. Immunization strategies on multiplex networks
Appendix G. Spectrum of the Supra-Laplacian

Multilayer networks is a rising topic in Network Science which characterizes the structure and the function of complex systems formed by several interacting networks. Multilayer networks research has been propelled forward by the wide realm of applications in social, biological and infrastructure networks and the large availability of network data, as well as by the significance of recent results, which have produced important advances in this rapidly growing field. This book presents a comprehensive account of this emerging field. It provides a theoretical introduction to the main results of multilayer network science.