Networks: An Introduction Mark Newman Oxford University Press 784 pp. (2010) ISBN: 978-0-19-920665-0
	Reviewed by Luis H. Favela Department of Philosophy Center for Cognition, Action, and Perception, Department of Psychology University of Cincinnati Email: favelalh (at) mail.uc.edu

Network theory arguably has its origins in Euler’s (1741) graph theory, which was first developed in the mid-1700s to solve the Königsberg bridge problem. Since then, the basic units of graph theory—vertices and edges—have been utilized by a number of scientific disciplines to describe and analyze a wide variety of phenomena. Mark Newman begins his clear and comprehensive introduction to networks with a sampling of various kinds that have been studied: information networks such as the World Wide Web, biological networks such as neural connections, and social networks such as friendships among members of a club. As Newman highlights, network theory and methods are utilized not only within but also across scientific disciplines. The interdisciplinary nature of the scientific study of networks is a double-edged sword. On the one hand, it fosters the cross-pollination of ideas and methods across fields—for example, applying methods used to study computer networks to the investigation of brain networks (cf., Sporns, 2011). On the other hand, such interdisciplinarity can result in confusion and misapplication of theory and methods. Accordingly, Newman’s goal in “Networks: An Introduction” is to synthesize the current state of network theory into a “consistent language and notation” (2010, p. x, Preface). This is no easy task, but Newman gives an admirable attempt that is successful in many ways.

Newman begins with a brief introduction to basic network terminology, examples of networks, and properties of networks (Chapter 1). The rest of the book is divided into five parts. Part I (Chapters 2 to 5) consists of chapters dedicated to the definition and description of four classes of real-world networks: technological, social, information, and biological. Beyond explaining in great detail the aforementioned classes of networks, this portion of the book makes the case that network science is grounded in observational data. Thus, although modeling plays a substantial role in network science, the end goal is always to account for the behavior of real-world systems. Part II (Chapters 6 to 8) presents the quantitative foundations of network science. Whereas Part I attempts to motivate the idea that countless phenomena can be understood as networks (e.g., natural gas pipelines, citations between academic papers, and collaborations of actors—i.e., “Six Degrees of Kevin Bacon” [p. 54]), Part II begins to get into the nitty-gritty details of the conceptual and mathematical representations of networks. For readers interested in applying network theory, Part II provides a framework for researchers interested in putting network theory into practice. Newman begins with a clear explanation of how matrices and graphs lay the foundation for representations of networks. From there, he builds up to more complex types of network representations as hypergraphs and bipartite networks. While explaining the application of network theory, Newman defines foundational terms used throughout the network literature (e.g., degree, paths, components). Not only does Newman often pair terminology with multiple explanations or examples, he often provides visual representations of the concept in the forms of matrices and graphs as well as equations.

Part III (Chapters 9 to 11) discusses computational techniques and algorithms for analyzing networks. Chapter 9 discusses foundational issues related to analyzing networks computationally. It is here that one of the most important challenges of applying network theory arises, stemming from the interdisciplinary application of network science mentioned above. Newman claims that, “[m]uch time can be wasted when people fail to understand how a program works or misunderstand the kinds of answers the program can give them” (2010, p. 277). Just because the tools of network science can be readily applied to a phenomenon does not mean that just any kind of program or analysis will be appropriate. Not only can failures to correctly apply algorithms result in misinformation, it can lead to a drastic inefficiency in data analysis, as in the case of computing eigenvector centrality (pp. 345-354). Eigenvector centrality of vertex i in a network is defined as the ith component of the adjacency matrix’s leading eigenvector (p. 345). There are numerous ways to calculate the eigenvector. However, as Newman points out, such calculations can include a lot of unnecessary data and be immensely time-consuming. Treating eigenvector centrality with the power method is simpler, faster, and just as reliable as the standard linear methods (pp. 346-347). If a researcher is not aware of the mathematics behind the computational methods, then it is possible that she could waste time applying a relatively inefficient method. It is for that reason that Newman spends a substantial portion of the book going step-by-step to help the reader understand the algorithms at work in the computational software. Such understanding can help a researcher apply the appropriate tools and develop their own programs.

With the conceptual and methodological foundation put in place in Parts I to III, Part IV (Chapters 12 to 15) reviews specific models of network structure and patterns of connectivity, such as various types of random graphs (Chapters 12 to 13) and generative networks (Chapter 14), and more recent models such as small-world networks (Chapter 15). The final part of the book, Part V (Chapters 16 to 19), reviews various kinds of behaviors exhibited by networks. Whereas the previous chapters discuss network structures, the final chapters discuss the processes exhibited by those systems. Processes discussed include percolation and resilience (Chapter 16), epidemics (Chapter 17), dynamical (Chapter 18), and searching (Chapter 19). The material covered in Parts I to IV demonstrate that network science has a strong grasp of network structure. However, as Newman draws attention to, the processes of these systems are far from understood—such as nonlinear dynamics in brain networks (cf. Sporns, 2011).

“Networks: An Introduction” has a few, minor shortcomings. First, as an introductory text, it would be useful to have a glossary of network terminology and classes, as well as a list of equations and models for the different kinds of networks. Second, although it is useful to have problems at the end of each chapter, it would be more convenient to have solutions within the text instead of a separate solutions manual. Third, the abrupt ending of the book after a chapter on network search processes leaves room for a concluding chapter. A concluding chapter would be useful to review how the author accomplished the goal set out at the start of the book, namely, to synthesize the current state of network science into a “consistent language and notation” (Newman, 2010, p. x, Preface). Finally, although I can understand why Newman would not want to bias the reader with any one particular kind of software, some readers, especially the more novice to the field of network science, might want more concrete suggestions and sources for software tools (e.g., “Using your favorite numerical software...” [p. 392]). These shortcomings are very minor and do not detract from Newman’s achievement: an introduction to the burgeoning field of network science that is clear and easy to read and succeeds in presenting network theory and methods in a consistent language and notation. This book is appropriate for advanced undergraduate and graduate students from various disciplines interested in both the theory and application of network science. Newman has set the standard on which other introductions to network science will be measured.

References

Euler, L. (1741). Solutio problematis ad geometriam situs pertinentis [The solution of a problem relating to the geometry of position)]. Commentarii academiae scientiarum Petropolitanae, 8, 128-140.

Sporns, O. (2011). Networks of the brain. Cambridge, MA: MIT Press.