Below, a review I wrote on Vega-Redondo’s manuscript “Complex Social
Networks” for /Science and Public Policy /(Volume 35(9))

********

Complex Social Networks
(Econometric Society Monographs)
*Author: Vega-Redondo, Fernando
Cambridge University Press: Cambridge, 2007
ISBN 9780521674096*

Reviewer: Camille (Cami) D. Ryan, B.Comm, Ph.D.
Published in: /Science and Public Policy, Volume 35 (9), November 2008/

As a social scientist and a social network analysis enthusiast, I am always looking for new sources to cite and new material to enable me to push the boundaries of my thinking and to bridge into more complex analytical processes.

Vega-Redondo’s monograph /Complex Social Networks/ does just that. The monograph, published by Cambridge University Press as part of its Econometric Society Monograph series provides a well-organized overview of theoretical research that lies at the juncture of the study of complex networks and social network analysis. The study of complex networks has gained popularity over the last decade or so, founded in statistical physics, but is often foreign to researchers from other disciplines. /Complex Social Networks/ attempts to bridge the gap by providing the social scientist, looking to explore the intricacies of complexity, with an overview of the main issues and techniques associated with complex networks. Conversely, the monograph also provides the complex network theorist with socioeconomic references and examples as viewed through the economics lens.

In the introduction, Vega-Redondo suggests the interdisciplinary approach may be useful in the study of complex networks with a review of the range of applications and empirical evidence in the realms of: transportation networks, internet networks, information flows through citation analysis, biological networks and, of course, social networks. The author acknowledges that although there is some methodological convergence amongst these research areas, he does validate that they “…naturally maintain many specificities of their own”, particularly socioeconomic networks where “…environments cannot be ignored” (10). Vega-Redondo then provides illustrative examples of the latter including: labor markets, technological diffusion, social movements and recruitment, peer effects, R&D partnerships and networks of organizations. He then provides a checklist of features for identifying complex networks which enable the researcher to “…recognize qualitative features of large social networks that could have significant implications on how [they] operate in the real world” (11). Most significantly, Vega-Redondo outlines the three key forces that underpin network agent behaviour in nearly all interesting network applications: diffusion, search and play. These three factors serve as dominant themes throughout the monograph.

Chapter two provides a nice segue from the introduction to the remaining sections of the monograph. It presents the main concepts and basic tools of the modern theory of complex networks including definitions as well as network types and characteristics. The latter characteristics include an overview of qualitative features of networks illustrated through their measures such as geodesic distance, connectivity, cohesiveness and component size. The chapter then provides an overview of networks types: Poisson random networks, general random networks, small worlds and scale free networks. Chapter three takes the reader into the well-established field of research of epidemiology as an illustrative and quantitative examination of social phenomenon wherein diffusion (one of Vega-Redondo’s key forces) is propagated from one agent to another but is unaffected by the environmental conditions within which the two nodes reside. This is akin to biological infection and the author explores three frameworks that can explain this type of epidemiological network phenomenon: resilient diffusion (SI model), the reach of diffusion waves (SIR model) and long-run prevalence (SIS model). Chapter four provides a complimentary exploration of the diffusion and interaction (play) through neighborhood effects. In this case, diffusion relies on coordination efforts rather than simulation or reproduction which better reflects the realities and nuances of social phenomenon. Vega-Redondo presents the reader with the diffusion effects on random networks both in the context of permanent adoptive behaviour and temporary adoptive behaviour. What I particularly was pleased to see Vega-Redondo consider in this section was the notion of continuous innovation. Quite rightly, he looks at innovation as an endogenous consisting of the “…juxtaposition of different earlier processes of (partial) diffusion…” (145). Thus, Vega-Redondo quite rightly conceptualizes diffusion and play in networks as being both fueled by and dependent upon the persistent process of innovation.

Chapter five delves into the final force at work in social processes on large, complex networks: search. The search factor or function is an important one, driven by the problem-solving impetus. If one agent is unable to address an issue, he/she seeks to find another agent within the network that can. In large networks, optimizing the search function is further complicated by the scope of the networks of agents and, often, limited access to and ability to process information. Vega-Redondo also considers the happenstance wherein there are simultaneous pursuits amongst agents along assorted paths with varying objectives driving behaviour. The author’s exploration of this sheds light on how the topology of a given network encroaches on the delay problems of congestion in search endeavours. Vega-Redondo then looks at network design issues that outline network topologies that would optimize a given network. In the final chapter, the author considers, in combination, the three forces of search, diffusion and play in the formation of social networks within the context of a complex environment. This nicely rounds out the monograph, encapsulating concepts and methods outlined earlier with the real-world notion of endegenous network formation and evolution. Vega-Redondo balances the notions of search, diffusion and play and how they can drive network formation with the relationship between agents’ embedded behaviour and the overall evolution of the network. He delves into some of the representative instances of game theoretic models which illustrate how incentives affect problems of network formation: connections model, access model and coordination game model. He then studies them through the lens of static equilibrium lens but then moves into the dynamic long-run scenario in terms of network formation processes, challenging the linear access model and addressing the shortcomings of bounded-rationality learning in games. Vega-Redondo pulls the “complexity” card and explores scenarios through a variety of dynamic models “…where nonstationarity of the environment is made explicit and takes alternate forms” (26). In all cases, an interesting interplay between network design and strategic choice is uncovered that proves to be the determining factor in how well a given network can develop and maintain connectivity.

Rounding out the monograph is a series of three appendices which are referred to throughout the book. In them, Vega-Redondo provides detailed descriptions of the techniques utilized and outlined in the monograph. These three appendices, along with the introduction, are effective ‘book-ends’ to this body of work on complex social networks. Overall, /Complex Social Networks/ is a tight, well-organized reference book for complexity theorists and social network enthusiasts alike. Each chapter includes references to social and economic topics. However, most of the content revolves around highly mathematical processes that are part of the social phenomenon occurring within networks. This book is not for the mathematically faint-of-heart!

Nevertheless, the monograph is a good reference for the social scientist that wishes to expand his/her knowledge into the nuances of complexity theory and its often dense mathematical processes and also good for the purist complexity theorist as it illustrates real-world socioeconomic examples. Vega-Redondo’s conceptualization of three driving forces or themes in complex social networks, which are dominant elements of this monograph, is quite useful. While social and economic examples are referred to throughout the monograph, these more abstract concepts keep technical and theoretical approaches an arm’s length from particular domains and, rather, focus the reader on the notion of social processes in network-based search, diffusion and play activities.