This huge volume has 44 chapters written by more than 40 experts worldwide. The text focuses on the synergy between graph theory and combinatorial optimization, plus algorithms as a vehicle for practical implementation. That format is a bit unique and requires a modular structure; consequently, the text is a combination of papers from experts in graph theory, graph algorithms, and optimization. As a result, 21 chapters are devoted to graph theory, 19 deal with combinatorial optimization, and 24 deal with algorithms (the topics overlap in some chapters). The content is divided into several large research areas: graph basics, graph theory (including algebraic and structural graphs), special graphs (and planar graphs), along with topics in graph manipulation like petitioning. Apart from that, the text covers in significant depth advanced topics such as matroids and randomized graph algorithms. The latter are quite different from the well-known random graph model of Erdős-Rényi. For example, the most interesting chapter (31) discusses five problems in graph algorithms and presents randomized algorithms for each of them. The focus is on a Las Vegas randomized algorithm approach, which always produces results but expresses large variations of execution time. The next chapter adds value by presenting a hybrid analysis problem. The latter is a common denominator in combinatorial optimization, including the theory of submodular functions. In practice, hybrid analysis has strong implementations in building up partitioners for large-scale systems.

I must stress that this is not a textbook; there are no exercises to test concepts or specific knowledge. For example, the first three chapters provide an introduction to basic concepts and algorithms, graph-theoretic properties and algorithms, and methods for exploring the graphs. Due to the book’s size, even though introductory in nature these three chapters require preliminary knowledge on the subject. However, the extensive references and “Further Reading” may help the curious mind find a set of texts that may help with getting up to speed. The theorems and lemmas are clearly stated and the provided proofs are precise.

Overall, the book is an excellent and comprehensive text on graph theory, graph algorithms, and optimization. Obviously, due to its size and ambitious goal to present the synergy between three disciplines, the book lacks the structure and organization of a textbook. As such, the book cannot be used directly in a course (graduate or undergraduate). Instead, the text has value as a concise, very-well-written, and comprehensive guideline for researchers and graduate students.