The Nature of Complex Networks provides a systematic introduction to the statistical mechanics of complex networks and the different theoretical achievements in the field that are now finding strands in common.

The book presents a wide range of networks and the processes taking place on them, including recently developed directions, methods, and techniques. It assumes a statistical mechanics view of random networks based on the concept of statistical ensembles but also features the approaches and methods of modern random graph theory and their overlaps with statistical physics.

This book will appeal to graduate students and researchers in the fields of statistical physics, complex systems, graph theory, applied mathematics, and theoretical epidemiology.

Table of Contents1 First Insight 

2 Graphs 

3 Classical Random Graphs 

4 Equilibrium Networks 

5 Evolving Networks 

6 Connected Components 

7 Epidemics and Spreading Phenomena 8 Networks of Networks 

9 Spectra and Communities 

10 Walks and Search 

11 Temporal Networks 

12 Cooperative Systems on Networks 13 Inference and Reconstruction 

14 What's Next? 

Further reading 

Appendix A Adjacency Matrix for Hypergraphs 

Appendix B Spectra of symmetric normalized Laplacians of sample graphs 

Appendix C Generating Functions 

Appendix D Hyperscaling Relations for Percolation 

Appendix E Degree Distribution of a Damaged Network 

Appendix F Non-backtracking Matrix 

Appendix G Treating General Interdependent Networks 

Review

The current volume by Dorogovtsev and Mendes takes quite a broad view of complex networks to include the analysis of finite and infinite graphs, directed and undirected graphs, multigraphs, hypergraphs, and even simplicial complexes, as networks scale according to increasing N or in some other fashion. The writing style is that of physics and especially statistical mechanics with frequent connections made to physical concepts such as Bose-Einstein condensation...The current volume can especially serve as a useful reference on complex networks from a physics perspective. ― Lenwood S. Heath, MathSciNet

About the Authors

Sergey N. Dorogovtsev graduated from Leningrad State University in theoretical physics. He was a researcher at the Ioffe Institute, St Petersburg, Russia, from which he obtained a PhD, and at the University of Porto. Currently, he is a senior scientist at the University of Aveiro, Portugal. He is responsible for a number of results on the statistical mechanics of complex networks and on critical phenomena in disordered systems. 

José F. F. Mendes is currently Professor of Physics at the University of Aveiro, Portugal. He studied at the University of Porto from which he graduated in Physics in 1987, and obtained his PhD in Physics from the University of Porto in 1995. He then completed postdoctoral studies at the University of Boston in 1995/1996. He is Fellow of Academia Europaea (2012), Network Science Society (2019) and American Physical Society (2020). He has received the CSS Senior Scientific Award by Complex Systems Society (2020).