The modern study of networks has become a prototype of interdisciplinary research. Sociologists, computer scientists, chemists, economists, power engineers, transportation engineers, and a host of other communities whose problem domains consist of things in relation with one another employ networks as descriptive tools.

The analysis of networks as objects of study in their own right, rather than simply as natural representations for a domain, began within these different communities, but has recently become its own specialty. For the past decade, Newman, a theoretical physicist who started his career studying quasicrystals, has been demonstrating the power of tools from mathematical physics in studying networks. His earlier collection of classic papers on the subject [1] was a great service to newcomers to the field, who will now welcome his unified textbook on the theme. This volume distinguishes itself from other network texts by its attention to the breadth of both the areas to which networks have been applied and the techniques for reasoning about them.

The book is organized into five parts. The first part surveys networks as representations in four broad application areas: technological systems (such as the Internet, power grids, and road networks), social systems, information networks (including citation and hyperlinked networks), and biological networks. This detailed grounding in real-world problems will motivate many readers to explore the detailed formal exposition in the later sections.

Part 2 provides a mathematical toolbox for describing and reasoning about networks. Newman’s mathematical exposition is at once formally rigorous and pedagogically lucid. Coupled with the very practical orientation of Part 1, it will hold the attention of readers who might otherwise be impatient with detailed formalisms, and it should raise the standard of network discourse in communities where the focus is on the use rather than the theory of networks.

Most networks of concern today are so large that their study requires the use of a computer. Part 3 summarizes a range of relevant algorithms. Computer scientists will miss the accustomed pseudocode representation of algorithms, which Newman prefers to describe verbally, but the descriptions are unambiguous and accompanied with a careful analysis of computational complexity.

Part 4 describes various network models, including numerous variations of the random graph and a variety of models driven by specific growth models. These models cover the dynamics of a network as it forms. Part 5 discusses the dynamics of other processes constrained to operate on a network, including percolation, epidemics, more general dynamical systems, and search. One very recent area that is not explored in depth is the interaction between these two, in which processes on networks modify the structure of the networks themselves.

The volume includes exercises at the end of each chapter, a comprehensive integrated bibliography, and an index. It is likely to become the standard introductory textbook for the study of networks, and it is valuable as a desk-side reference for anyone who works with network problems.