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A.-L. Barabasi

posted on 06 September 2002

reviewed by Joseph Wakeling

"From a cocktail party to a terrorist cell," announces the inside-cover blurb, "from an ancient bacteria to an international conglomerate - all are networks, and all are part of a
surprising scientific revolution." It's a revolution of which Econophysics website regulars will no doubt be well aware, with new papers in this field appearing on the website as soon
as they are submitted to preprint archives. And among the researchers in this field, no name is more prominent than that of Albert-László Barabási.

Barabási's particular claim to fame is to have identified the existence of, and mechanisms that underlie, scale-free networks - networks where the probability distribution for the
number of links each node possesses follow a power law. While the most often-quoted example is the internet, other social networks also follow this rule, as do protein networks
and the metabolic network of the E. Coli bacterium - and the whirlwind of new work that has followed the original works by Barabási and colleagues shows no signs of abating. In
Linked, Barabási aims to present this work to the wider public, setting it in its proper historical context as a development of classical graph theory, and at the same time, in terms of
its implications for our everyday lives.

The book can be divided, roughly speaking, into two parts. The first deals with the theoretical aspects of the subject - the history of graph theory, from Euler's "Königsberg problem"
proof, through Erdös and Rényi's famous work on random graphs, the more recent work on "Small World" networks and, finally, the story of Barabási's own work that led to the
development of models for scale-free network formation. It's all very clearly explained for the most part, with plenty of interesting anecdotes and stories surrounding the
development of the different theories; particularly nice is Barabási's use of footnotes to impart some of the mathematics at work, allowing those who are not interested to read on
uninterrupted while providing extra insight to those anxious for more.

The second part of the book crosses over to discussion of examples and implications of the work in the real world - a wide range of topics, from the spreading of viruses (both real
and computer-based) to protein and metabolic networks in biology, the economy, and the organization of terrorist groups such as al-Qaeda - and, of course, the development of the
internet. Perhaps most interesting is the discussion on the way these systems' strengths and vulnerabilities can be linked back to fundamental dynamics of scale-free networks:
robustness against failure, but extreme vulnerability to targeted attack.

It has to be said that occasionally Barabási goes a little overboard with some of his case studies - for example, in Chapter ("Link") 10, jumping at the chance to make a
contraversial statement about how we should distribute AIDS drugs (targeting the promiscuous) while conveniently forgetting that, as he himself states a couple of paragraphs
earlier, these drugs don't actually cure AIDS! And occasionally, too, the prose can get a little wearing - the division of each chapter into short numbered segments makes it read,
sometimes, more like a collection of short pieces without much continuity as a whole. (In many respects, it's a work that is better to dip in and out of than read all the way through.)
Nevertheless, Barabási's interesting and wide-ranging choice of examples, from denial-of-service attacks on the internet to the spread of Christianity, combined with a nice set of
amusing anecdotes, clear explanations and the obvious benefit of an "insider's view" on the subject matter (plus the aforementioned mathematical footnotes, which are easy to
grasp and, though brief, give you all the essential details), make Linked a book that is well worth reading.