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Networks: A Very Short Introduction (Very Short Introductions)

Caldarelli, Guido and Catanzaro, Michele
Oxford University Press: Oxford, 2012
ISBN 9780199588077 (pb)

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Reviewed by Patrick Doreian
University of Pittsburgh and University of Ljubljana

Cover of book This book must have been difficult to write. Certainly, it is difficult to review fairly because of the size limitations imposed by Oxford. Despite an engaging writing style and casting a wide topical net, it was impossible for the authors to overcome the severe constraint implied by this being a 'short introduction'. Necessarily, topics must be omitted and the coverage of what is included can only be superficial.

It is hard to discern the intended audience for this volume. Areas I know well - structural balance (p. 21) and structural equivalence (p. 112) - are presented in a trivial and misleading fashion. Worse, areas I do not know well - e. g. protein networks (p. 24) and food chains (pp. 28-9) - but seem potentially interesting were covered in inadequate ways for a general reader.

The physicist slant is revealed early by declaring (p 6) a focus on "complex, emergent, and self-organizing systems" within which "networks are becoming increasingly important as a universal mathematical framework, especially when massive amounts of data are involved". The seductive allure of large networks, often with little by way of genuine substantive content, drives much of the emphasis on the topology of networks in 'network science'. The authors do turn belatedly (p. 108) to dynamics and network processes. Having less on topology and more on dynamics would have been a better informative strategy.

The history of fields necessarily is given short shrift in such a brief introduction. Much of the early work in social science was ignored. That approach could have been extended usefully by eliminating the description of early work by physicists including details of random graphs, lattices, short cuts on grids, using simulation superficially, and the slavish repetition of the 'bow-tie' diagram (p. 44). The last item was constructed to characterize the World Wide Web (WWW) and had some value. But the authors write: "This complicated structure is not specific to the WWW, but it appears, with different components, in all directed networks". This glib claim points to an imperialist impulse.

Glibness is a general feature of this book. After a description of random graphs, there is: "If we want to compare the abstract model with the real network, we now just need to compare the measures in both cases (p. 12)". The authors do not deliver this comparison effectively. After discussing degree, the term 'circle' is inserted misleadingly and coupled to the concept 'core discussion network' (p. 19). The brief discussion (p. 32) of Facebook and LinkedIn, coupled to companies targeting 'influential' individuals borders on triviality. Prefaces such as "sociologists have identified ..." and "sociologists argue ..." (with no supporting evidence) - seem designed to assert some legitimating cover for statements that follow.

Much is made of network science - yet it is not defined. Emphasis is placed on small-world phenomena and power laws without defining them: definitions are replaced by allusions. The idea of fat-tails in degree distributions as indicators of heterogeneity is useful. But the authors add: "mathematically speaking, the shape of a degree distribution is well described by a curve called a power law (p. 61)" and "a strongly skewed fat-tailed distribution is a clear signal of homogeneity even if it is never a perfect power law". This is less than helpful.

The author’s coverage of transitivity and clustering is trivial. Presenting the self-evident fact that real and random networks differ has little value. They add "this suggests that some non-trivial process, possibly a form of self-organization, is at work in generating this extra transitivity (p. 84)". Regarding rewiring lattices they argue weak ties "could be at least partially matched with Watts and Strogatz’s shortcuts (p. 53)". The authors write "evolution seems to have selected motifs, because of their optimal properties (p. 91)". Using the words "suggests", "could be", and "seems" is, at best, vague. Worse, they are used to imply a universal applicably that is not merited.

The self-congratulatory blurb from Oxford on the inside cover quotes a reviewer describing their series as a "thinking man's Wikipedia". It is not. Despite its faults - inaccuracies, biases, and incompleteness - Wikipedia is self-correcting and provides useful sources for readers to consult. The references provided in this book are to complete books - with a strong bias towards physics - and do not include the book’s very interesting examples. There are no details about the source for the food web shown in Figure 1. Laumann and Youm’s work on sexual networks is described (incompletely on pp. 80-2) with no citation for readers to follow. These are examples are not alone.

Alas, there is little about this slim volume to recommend it to general readers.


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