Customer Reviews

Small Worlds

5 star:		(1)
4 star:		(3)
3 star:		(1)
2 star:		(2)
1 star:		(0)

 

 

I read the review in New Scientist, and liked the sound of this book. When it arrived I read the blurb on the back, and was further encouraged by the fact that a Sociology Professor was encouraging students to read it. I was therefore expecting a reasonably tough but rewarding read (my math is at undergraduate level and somewhat dated, but I do make an effort). Instead with the exception of a few pieces of commentary, particularly at the beginning, I found the book virtually impenetrable because of the denseness of the mathematical modelling techniques used. I suspect this is one strictly for the experts, and those with excellent post-graduate math skills.

Networks are since a couple of years object of intense research in several different disciplines. One reason therefore is certainly the outstanding article by Watts and Strogatz, Collective dynamics of small world networks, Nature, 393:440--442, 1998. Unfortunatelly, this book can not continue the high level of this article. Actually, it does not really provide much more information than the article itself. I would suggest to read the article cited above and either decide for another book or to look directly in the literature and read the origninal articles.

To summarize, this book is not terribly weak, but one can clearly sees that it swims on the current 'complex networks' wave without providing enough justification for its existence. Of course, if you do not have access to the original literature and just what to have a general overview of complex networks and what be done with them, you may consider buying this book.

This book is very hard for non-numerate individuals (like myself, a law student). I picked it up after reading Six Degrees: The Science of a Connected Age (Open Market Edition), hoping I would find longer - but equally accessible - explanations of those concepts that are sketched in the latter.
Unfortunately, I didn't. The book is essentially a presentation of the modelling techniques used by Prof. Watts in arriving to the theory of Small Worlds. A thorouhg understanding would require truly firm foundations in statistics, graph theory and topology. Without that, you'll probably be able to understand at most twenty pages (out of 241).
If you have read Six Degrees, you'll still find some useful and still accessible discussion on multidimensional scaling, i.e. on the problem of measuring social distance, which Watts later discusses in Six Degrees with reference to the problem of search in networks. However, that's just about it.
My two-star rating is by no means meant to criticise Prof. Watts's ideas, or the substantial contentions he makes in the book (very few of which I was able to understand from a mathematical point of view, due to my faulty background). Deserving two starts, instead, are the Editorial reviews, which are hugely misleading. This is not "aimed at a wide audience". Or, better, it is aimed at a wide audience of MATHEMATICIANS. It is a technical one, and that would need to be made explicit.

Mathematical level: Moderate; there's no calculus, and little high level math, but the book is quite mathematical in tone, and some of the arguments may be difficult to follow without a good "math sense". There are MANY equations and graphs.

Good points: Watts covers an area that will interest those who deal with mathematical models of social networks e.g. models of disease-spread, especially HIV. It might, however, cover other things that can spread through networks as well. He presents analysis of graphs (or networks) that are neither random nor highly structured; and begins to examine ways that the degree of structure v. randomness can be measured.

Bad points: There are more than the usual number of typos. The models presented are a "first step", only.

The author believes that human thought might be a small world, in the sense that one could reach any idea if he/she finds the right associations and "short-cut"s. The small-world theory is indeed one of those short cuts itself. It links many different domains and uncovers some interesting common behavior.

The theory is developed in a scientific manner with extensive numerical support. Rich literature reviews and many open questions make this book a good research reference. Complex observations are generally followed by qualitative explanations. However, some of the simpler derivations are not fully clear. I believe that adding a few lines here and there can turn this book into a textbook.

The book spans many different areas of science and a deep understanding of the related results may require some background. However, each chapter ends with a brief summary, allowing the reader to move forward if he/she finds the chapter difficult. In summary, as the author puts it, the book is simply the "end of the beginning" in an exciting new field.

The book basically gives all the details needed to understand Watts and Strogatz famous Nature article 'Collective Dynamics of Complex Networks' in 1998. I think that it is basically Watts PhD-thesis and as such it is of course nicely written, but nothing for the laymen who is rather referred to Watts other, more story-telling book 'Six Degrees', Barabasi's book 'Linked', or to another book that I would recommend most, namely the one by Mark Buchanan titled 'Small Worlds'. Mark is a skillful scientific writer and his book has a broader scope that makes it more interesting than each of the two monographs that are a bit more focused on the scientists own contribution.

The book takes a systematic look at the 'small world' graphs. These natural graphs have been discovered by graph theoretist as erly as 60's, but were not properly understood. The graphs are remarkable in their ability to cluster and scale lengths. There are fundumental connections between these graphs and complex systems, discrete dynamical systems, computation and information processing. Duncan has done a tremendous job in building experimetal and theoretical models trying to understand how these graphs come about and sustain themselves. Read this book.