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Fundamentals of complex networks : models, structures and dynamics
Chen G., Wang X., Li X., Wiley Publishing, Hoboken, NJ, 2015. 392 pp. Type: Book (978-1-118718-11-7)
Date Reviewed: Nov 25 2015

This textbook covers the area of complex networks; as such, it is long overdue. Complex networks (and complex adaptive systems, two terms that are very close) are one of the most fundamental and significant areas of research in 21st century science--regardless of the area. Whether one is active in economics or sociology, medicine or computing, physics or biology, complex systems, networks, and so on have been the most significant development for many decades and will continue to drive forward our understanding of all areas of science, engineering, technology, and processes.

Luckily for us, our three authors have done a fine job of creating the first comprehensive textbook for this field. The preface states:

This book has been designed to serve as a concise textbook for newcomers to the field. It is written as a one-semester introductory text for upper-division undergraduate or first-year graduate students in natural science, mathematics and engineering, or as an edited volume for self-study, or as a handy reference for research.

While the book is quite full of some nontrivial mathematics--take care all ye fainthearted, math-shy social scientists--it is quite readable and understandable; that being said, some background in math is really needed.

Networks tend to be dynamic; complex networks, even more so. Those networks build up into systems that are in some way self-adaptive (very common in economics, traffic, and the spread of infection, to name just a few). This complexity, as per our authors, takes various forms: structure complexity, node-dynamic complexity, and mutual interactions among various complex factors (this latter example has become common when dealing with risk assessment/management in international political issues). Systems also increasingly couple, thus increasing complexity, sometimes exponentially and frequently unexpectedly--the most powerful type of these phenomena is spatiotemporal coupling of networks/systems.

The authors’ discussion begins with a historical picture of how the field developed. This aspect of the book alone is a very interesting study (no math here). If for nothing else, the book is worth reading for this chapter. The discussion summarizes with the following statement:

Many traditional theories, methodologies and techniques, meaningful and efficient for small-scale computation and analysis, are no longer applicable to such giant networks. The interactions among nodes and between different levels of the complex structure of a huge network generate many unexpected or unpredictable behaviors, such as emergence and chaos, going much beyond the traditional thinking of networks as simple and steady graphs.

The book is divided into two parts. The first part is general, providing fundamental theory; it is composed of three chapters. Each chapter in Part 1 ends with exercises and references. The second part shows various applications; there are six. The authors state that of these case studies, it will be rare for a single person to have a need for more than one or two. I agree. Each chapter of Part 2 ends with references. Next is chapter 10, “Brief Introduction to Other Topics,” which is quite apropos and well done.

I must note particularly Section 10.7, “Cascading Reactions on Networks.” If I am correct in what I said above about the centrality of network research to almost every knowledge field today and in the foreseeable future, then the concept of network cascades is, within that, one of the most difficult and yet most significant of all the areas. Of what area should everyone be aware? Electric power generation and distribution networks! We must all be aware today of cascades of failure with the most egregious effect resulting (we hope not) from a national-level electromagnetic pulse attack. Such a cascade has the potential for an enormous disaster. As issues of cascade was one of the prime reasons I desired to read and review this book, I was tempted to quote extensively from this subchapter--I have restrained myself in the interest of brevity. This subchapter is particularly well written and well referenced, and an area of great complexity is very well explained, simply and briefly. Again, if for nothing else, this book is worth studying in order to comprehend this single section.

The book is very well illustrated throughout.

I do have one issue, however, with the book, but with the publisher and not with the authors. For some ridiculous reason, they used a really nasty font that made the book particularly difficult to read.

I am quite pleased to recommend this book.

Reviewer:  Mordechai Ben-Menachem Review #: CR143973 (1602-0105)
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