This book is a development of Performance Analysis of Communications Networks and Systems of 2006. Its current incarnation has a broader scope, extending to complex networks, the broad term covering all types of real-world networks, that encompass communications networks. Apart from the correction of numerous errors in the earlier book, nearly all chapters have been extended. Chapter 17 on Epidemics in networks has been added, while the appendix on algebraic graph theory has been deleted, because our book Graph Spectra for Complex Networks amply replaces this chapter. Similar to Graph Spectra for Complex Networks, art. x has been used to refer to article x in Appendix A. The number of problems, together with their solutions in Appendix B, has been doubled at least.

Performance analysis belongs to the domain of applied mathematics. In particular, the branches of mathematics as probability theory, stochastic processes and graph theory are exploited, besides analysis (calculus) and linear algebra that are omnipresent nearly everywhere. The major aim of this book is to offer several mathematical methods to address challenges in network science, the rapidly growing field of complex networking. The link with technology is kept shallow, on purpose, because most technical advances in micro-electronics, in communications protocols and services, standards, etc. have a more limited lifetime and a narrower scope compared to mathematical concepts.

This book aims to present methods rigorously, hence mathematically, with minimal resorting to intuition. It is my belief that intuition is often gained after the result is known and rarely before the problem is solved, unless the problem is simple.