When someone mentions network optimization, network flow is probably the first thing you think about. However, the maximum flow problem, first solved by Ford and Fulkerson [1], and its generalizations, such as the circulation problem, are not the topic of this monograph on network optimization. The author, Peter Whittle, an emeritus professor of mathematics at the University of Cambridge, instead focuses on the optimization of the network structure itself.

The first half of the book deals with flow networks, but it does so from a peculiar point of view. The author describes how the structural design of such a network can minimize its cost subject to a given set of constraints. This is applicable in conventional transportation networks, but also in heat dissipation and engineering structures. His formal treatment of the former proves that direct straight-line links from sources to sinks solve the classic transport problem, and that variable loads provide an incentive for hierarchical trunking to achieve steady flows, as exemplified by the public switched telephone network. A continuous generalization of flow networks is illustrated with an optimal cooling example, and civil engineering structures and bone structures provide nice, insightful analogies. Of course, road networks, congestion, and Braess’ paradox [2] also make a brief appearance in this part of the book.

The second part focuses on artificial neural networks and is completely disconnected from the previous chapters. In three short chapters, the author surveys supervised learning (specifically, the back propagation algorithm) and a variety of network models, such as Hamming nets and Freeman oscillators.

The third part of the book turns its attention to processing networks, such as those found in scheduling problems. This discussion relates more to the traditional fields of queueing theory and job shop scheduling in operations research than to network optimization and design.

Finally, the last part of the book is devoted to communication networks, both circuit switched (or “loss networks,” in the author’s terms) and packet switched. A final chapter is dedicated to the World Wide Web (WWW) and its scale-free structure, with references to the renowned Barabási-Albert model [3] and the author’s previous work on polymer models, which is described in detail in a separate appendix.

This book might be too formal for undergraduate computer science students, since it focuses on mathematical properties, theorems, and proofs, rather than on algorithms. However, it might be valuable for graduate students and researchers. It should be noted, however, that the author’s terminology might sometimes be confusing to computer scientists. For instance, the terms “evolutionary algorithm” and “evolutionary optimization” are used in a sense that has nothing to do with their meaning within the artificial intelligence (AI) field. With this caveat in mind, the mathematically oriented reader might get some useful ideas and suggestions from the analogies and formal results presented here.