Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton Studies in Complexity, 36)

More intense on statistics than stories.

Certainly one of THE books on the math topic of Small Worlds. Well organized and presented. I consult it from time to time.

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.

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.

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.

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.

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.

この書物は自分の周りにたった５人いれば世界中の人とネットワークができ上がると言うスモールワールドを実験検証したダンカン・ワッツのペーパーバック版である。　ネットワーク理論の書物は数あれども、たとえそれに興味をもっていても生物学者にとってはなかなか取り付く島がなかった。スチュワート・カウフマンの「自己組織化と進化の論理」と読み合わせるとかなり理解ができ、なるほど「ザ・ガッテン」と納得がゆく部分が多く読んでいて嬉しくなる書物であった。　そもそも世の中の様々な現象、あるいは生物学のなかでも化学反応系や遺伝子やタンパク質のネットワークが最近注目され、それらのデータバンクやソフトウエアも多数用意されている。バイオインフォーマテイックスやデータマイニングの新しい分野にコンピュータは必要であり、また多少の数式を理解する必要がある。　英文は少し我慢して慣れて来ると、とても読みやすくて、大敵の数式もくり返しながめていると少しずつでも分かってくるように記述されているのが入門者には嬉しくもあり楽しい。　内容は誠に充実していて読み応えがあるが、できればCDやネットワークを解析するソフトなどが付録としてついているとなお嬉しくなるそんな書物であった。