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Networks pervade our lives. As graphs representing interconnected systems, they can represent social interactions, economic relationships, power grids, computer networks, Web links, bibliographic citations, or biochemical processes. Whether the networks are social, economic, technological, or biological, their study has spurred a lot of interest over the past decade or so.
The Web established a market for many popular books on networks. Some of these have been entertaining and informative—for example, Duncan Watts's Six Degrees or Albert-Laszlo Barabasi's Linked. However, they aren’t rigorous enough for more demanding readers. Those wishing to plumb the depths of networks have had to make their way through countless research papers, which necessarily offer a fragmented view of any field. Even worse, network research terminology is often confusing, given the youth of this field and the different specialties contributing to it. Hence, Ted G. Lewis's textbook offering a panoramic view of this emerging research area is welcome.
The Mathematics Behind Network Models
According Lewis, network science reflects the combination of graph theory, control theory, and cross-discipline applications. Calling it a science, however, is probably an overstatement—the kind of hype that has made some people dismiss network research as a passing fad or fabrication, ignoring important lessons this field can teach us.
The subtitle might also be misleading. Lewis has written the book with graduate students in mind, so it's more theory than applications. This is partially justified because Lewis has tried to separate the wheat from the chaff to produce a valuable textbook. In this yet-to-mature field, theoretical models are the wheat while particular applications are usually the chaff. This is because new observations and a better understanding of the studied processes often make research results obsolete in a quite short period of time.
After some introductory material on the historical roots of networks and a brief overview of graph theory, Lewis analyzes some of the most popular network models that researchers have proposed to formulate hypotheses about observed phenomena. These range from Watts-Strogatz small worlds and Barabasi-Albert scale-free networks to flow, influence, and netgain networks.
Traditional graph theory has typically focused on network static properties, which Lewis also uses to study different network classes. However, modern network models focus on the dynamic behavior of interconnected systems. Lewis concentrates on four network properties:
- emergence—the process whereby a macroscale (global) property emerges as a consequence of the repeated application of microscale (local) modifications.
- epidemics—the propagation of a signal (for example, contagion) through a network.
- synchrony/stability—the synchronization/stabilization of network nodes under changing conditions, which includes the study of conflicts and group consensus in influence networks, for example.
- vulnerability—the potential impact of node and link failures (for example, in the power grid), as well as the protection of the stability in Kirchhoff (flow) networks.
The final chapters turn to economics and biology as promising application domains for network theory. Lewis posits that netgain networks might be useful models for investigating how economic markets behave, that while biological network models show promise as research tools.
Style pros and cons
Lewis has made an extraordinary effort to provide a first textbook in this fascinating field. However, being first also has some disadvantages. Apart from typos that might be unavoidable in a first edition, especially if publishers want to cut proofreading and editing costs, I found some explanations more convoluted than necessary, even misleading at times. For instance, when discussing a classical paper on the Web topology as a directed graph, Web links are mistaken for physical network connections. Web nodes—that is, Web pages—are incorrectly identified as "nodes that send messages such as email" (page 159). Fortunately, such glaring errors are few, but they're unsettling in any textbook because they raise some doubts about its overall rigor and thoroughness.
The text is generally clear, but somewhat wordy and repetitive. The book feels as if it's written from course notes. Some repetition is desirable and even necessary in oral presentation, but it isn't as welcome in written form. For instance, the detailed introductions to each chapter almost summarize all the material in the chapter itself, thus virtually removing any pleasant surprise you might find from delving into the details. I find detailed summaries more useful at the end of chapters, rather than the beginning.
Lewis concludes each chapter with some exercises as well as interesting issues—even open research questions—that are "left as an exercise to the reader." He provides some Java software tools that support the exercises. (He even discusses some code snippets in the text—something I thought often distracted from the main discussion.) The software tools are invaluable for readers to experiment on their own, because many network issues can only be resolved through computer simulations followed by some curve fitting. All in all, I would recommend Lewis's textbook for graduate students and professionals with a keen interest in network models. Those with a more general interest might start with the popular books, then proceed with this book for a more thorough study. Despite its theoretical slant, casual readers can easily skip the mathematics and still glean much from this book.
Fernando Berzal is a member of the IEEE Computer Society and a senior member of the ACM. Contact him at firstname.lastname@example.org.