The Power of Networks: Six Principles that Connect Our Lives

A search on MathSciNet for papers with “networks” in the title returns 37,746 results. Searching “networks” on Google Scholar returns over four million results. Network science and its mathematical underpinnings is a highly active area of current research that spans across many disciplines and has a great number of applications. A particularly nice survey of network science from the mathematical point of view is given in the article “Network Analysis” by Esteban Moro in the Princeton Companion to Applied Mathematics. Moro writes

The analysis of networks is an old subject in mathematics, and it has its roots in many other disciplines, such as engineering, the social sciences, and computer science. However, in recent times the digital revolution has brought with it easier access to detailed information about phenomena such as biological reactions, economic transactions, social interactions, and human movement.

Since the study of biological reactions, economic transactions, social interactions, and human movement all involve the use of network theory, this quote serves to illustrate the significant role in which networks play in modern research, technological innovation, and understanding the world around us and our place in it. Given the ubiquity of networks and network science it is clear why Christopher G. Brinton and Mung Chiang would feel compelled to write a book on networks addressed to a wide audience. Their book The Power of Networks explains networks in a way that is accessible to readers that do not necessarily have a background in science, engineering, or mathematics, and focuses mostly on the technological aspects of networks.

The authors approach the subject of networks via six themes, which they call principles, that illustrate the way in which networks are used to solve problems or increase understanding of certain types of phenomena. In fact, the book is divided into six parts, with each part addressing one of the six themes. These themes are

• sharing is hard,
• ranking is hard,
• crowds are wise,
• crowds are not so wise,
• divide and conquer, and
• end to end.

These themes are illustrated by problems such as distributing signals across a communication network, Google page ranking, Netflix movie recommendations, viral internet videos, traffic routing, and six degrees of separation respectively. Furthermore, the authors describe how the six themes unify many different types of problems that can be addressed through network theory.

The Power of Networks is a well-written and engaging book that I think many readers will find interesting and insightful. The authors use a lot of illustrations and graphs, analogies from common experience, and worked out numerical examples to guide the reader to understand what are some times fairly technical concepts. An good example is the authors explanation of the Google PageRank algorithm in their Chapter 5 on ordering search results. In addition, Brinton and Chiang maintain a webpage that provides access to supplemental material often referenced in the text that provides further detail on many of the concepts described in the book.

Another feature of The Power of Networks that I think many readers will find interesting is that each of the six parts of the book contains a summary of the main points from to help the reader see the forest for the trees. The book also contains several interviews with leading figures from technological enterprises in which networks played an important role in innovation. An example is Eric Schmidt who served as the CEO of Google. These interviews expose the reader to the historical and human side of networks.

Overall, The Power of Networks is a nice book that I believe many readers will enjoy, especially readers interested in modern technology, engineering and innovation. For readers that are more mathematically inclined, it also does a nice job of explaining important topics from mathematics, such random graphs and the Watts-Strogatz theory, and what these ideas have to do with networks. If you have any interest in network theory at all, I recommend this book. Even if you start reading and find yourself getting bored with one section, keep skimming and you are likely to find something of interest.

Jason M. Graham is an assistant professor in the department of mathematics at the University of Scranton, Scranton, Pennsylvania. His current professional interests are in teaching applied mathematics and mathematical biology, and collaborating with biologists specializing in the collective behavior of groups of organisms.