Since the first ideas on how to describe existing networks with the mathematical tools of random graph modeling were revived in the context of Internet networks by the Faloutsoses, the new field of network science was born. Two types of books are published in this area. One considers positions from a modeling viewpoint and focuses on potential applications and consequences of the elaborated models (for example, Lewis’ book [1]); others--authored by mathematicians, physicists, or research-oriented engineers with a strong inclination to theoretical modeling (such as Van Mieghem [2])--deeply dive into the mathematical aspects of random graphs without maintaining a strict relation to the current practice. Obviously, both types are necessary for progress in networking. Van der Hofstad’s book follows the second avenue, which is not surprising--it was published as part of the distinguished “Cambridge Series in Statistical and Probabilistic Mathematics.”

In chapter 1, the author briefly discusses the basic results and concepts in the historical research context of complex network modeling (for example, small-world and scale-free phenomena are covered, as well as clustering problems; some classical examples are given as well). Chapter 2 introduces basic theoretical notions applied in modeling throughout the book: convergence of random variables, coupling, stochastic ordering, probabilistic bounds, martingales, relation of extreme value theory, and order statistics. Branching processes are covered in chapter 3. Then, types of random graphs are discussed: the most classical Erdös-Rényi model is covered in chapters 4 and 5. The former focuses mainly on modeling of the giant component, while the latter deals with more complex probabilistic properties. Chapter 6 introduces the concept of the so-called generalized random graphs aimed at making the Erdös-Rényi model more suitable to real-world networks. On the other hand, chapter 7 discusses graphs where all of the nodes are characterized with the same degree. The model associated with the creation of scale-free graphs, that is, preferential attachment, is covered in chapter 8.

For readers who find the modeling too simple and want extensions of the concepts presented, it is worth mentioning that the author prepared a book satisfying such expectations. It is accessible in electronic form via his web page. The book is written in quite a formal way and requires a lot of background knowledge on probabilistic modeling. Therefore, I can recommend it mainly to advanced researchers. However, it is thoroughly prepared as a textbook, with interesting suggestions for further discussion and exercises at the end of each chapter. A long list of relevant references is helpful for those interested in extending their knowledge of the presented results. This way, it can be successfully used as a basis for doctoral courses or even in the curricula of some graduate studies (mathematics or physics rather then engineering).