The Nature of Complex Networks

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.

1 - 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?

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).