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Complex Social Networks (Econometric Society Monographs)

Vega-Redondo, Fernando
Cambridge University Press: Cambridge, 2007
ISBN 9780521674096 (pb)

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Reviewed by Josep M. Pujol
Department of Epidemiology and Center for the Study of Complex Systems, University of Michigan

Cover of book This monograph provides a systematic account of theoretical research that lies at the intersection of the study of complex networks and social network analysis. It reviews the basic methodological framework used by network theorists, who are mostly physicists. Although the author successfully links each chapter to domains relevant to socioeconomic topics, the bulk of the book is a mathematical description of the processes inspired by social phenomena that take place in networks.

This book does not attempt to convince the reader of the relevance of network-based phenomena in social environments and the need for interdisciplinary approaches. However, the reader will still find justification for this interdisciplinary approach in the introduction in the form of several examples of socioeconomic phenomena that can be studied from a network viewpoint. The author moves quickly to his core objective: a detailed analytical description of social processes using the mathematical techniques developed by network theorists. Unlike other books, the author does not analyze particular examples, but rather focuses on what he claims to be the essential forces at work in social processes on networks: diffusion, search and play. This conceptualization, in my opinion, is useful for it allows for abstraction from the details of a particular domain and emphasizes a functional decomposition of social processes in these three building blocks.

The author provides an overview of the basic theory of complex networks in chapter two. The author introduces network concepts such as clustering and distance that will be extensively used in the rest of the book, as well as the basic networks models detailed in the literature of complex networks. This introduction is essential for those people not familiar with complex network techniques, which are mostly statistical physics. To the reader lacking proficiency in generating function methods and mean-field theory, the mathematics in this book might be overwhelming, but this is what complex network theory is about. The introduction and three appendices provide a description of those techniques, and the subsequent chapters offer examples of their application. This chapter and the appendices provide a short and intense introduction to the complex network theory on which the rest of the book strongly relies. Although chapter two is quite comprehensive, it would benefit from a more detailed description of the structured network models and the characteristics exclusive to social networks such as degree-correlations, assortativity and community structure.

The author then introduces the three essential forces that take part in social processes that occur in networks. The pattern is similar in the remaining chapters. A simple model of a process is introduced and formally derived. This process is iterated, adding more complexity to the agents and the network structure. In doing so, the author illustrates the effect of the network structure on the social process of interest, and at the same time demonstrates the application and limitations of a wide range of mathematical techniques.

Chapter three and four deal with diffusion, the process by which one agent changes its state according the states of its neighbours. Chapter three focuses on epidemic diffusion processes where the change of state is based on total exposure and diffusion occurs by contagion or by imitation depending on whether we are looking at diseases or fads. The author reviews the literature on diffusion waves and resilience for different network topologies, as well as the effect of interventions. In the following chapter, the adoption rule is changed to be a function of a game played with the agent's neighbourhood, thus diffusion relies on coordination rather than imitation. Throughout this chapter the author introduce spin models to show how system level diffusion depends on the delicate trade-off of the agents' local coordination process and the balance between heterogeneity and uniformity of the network structure.

Chapter five introduces search, the process of finding a target agent allowing only messages between neighbouring agents. Although the most common instantiation of search in the literature is routing, the author prefers to link it to organizational theory to emphasize the socioeconomic perspective of the process. Domain of application aside, this chapter describes the methodology to study the delay in the search, and how certain structural properties and the level of information available to the agents affect the time delay. As expected, this chapter also deals with congestion, which is an unavoidable factor if agents are in a realistic environment where time and resources are finite. The author shows how the heuristics and certain network structures well suited to spread the information suffer from an unbalanced workload of certain agents due to the underlying network structure. The last part of chapter five is devoted to this issue and the optimal network design that resolves the trade-off between time delay and congestion.

Up to this point the book has dealt with static network; in this last chapter the author reviews different models addressing the formation and evolution of those structural properties that characterize complex social networks. First, the author reviews different models based on game theory, where the structure arises as a result of the strategic game played by fully rational agents. The author discusses at length the shortcomings derived from the unbounded rationality assumption and the static equilibrium configuration. The rest of the chapter assumes - quoting the author - a more 'phenomenological' approach. These models illustrate the co-evolution of the network structure, by simple rules of link formation, and the agents' behaviour, either by playing games or by searching.

Fernando Vega Redondo has done a terrific job putting together a monograph that could be both a review of the current research and a reference book of the theoretical foundations and applications of complex networks. Needless to say, this is not an easy read, particularly for those who are not already familiar with the mathematical techniques. However, for those with interest and/or with mathematical training the book provides an in-depth look into network-embedded social processes.


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