Albert Barabasi presents the lay reader with a stimulating description of the origins of network theory and recent applications. He describes random networks, small world and scalefree networks. In nonrandom networks the importance of hubs is emphasized. Small world networks are the ones with a well defined averge number of links, and in scalefree ones the density of links scales as a power law. For the many interesting examples discussed, I would like to have seen graphs showing scaling over at least three decades in order to be convinced of scaling. However, in practice, whether a network scales or not may not be so important. I liked best the discussions of terrorism, AIDS, and biology. If one could locate the hubs, then a small world network could be destroyed, but as the author points out there is no systematic method for locating the hubs. Also, destroyed hubs in a terror network might be replaced rather fast, whereas airline hubs could not be replaced so quickly. The book might be seen as indicating a starting point to try to develop a branch of mathematical sociology. For example, the maintainance of ethnic identity outside the Heimat is discussed in terms of networking. Now for a little criticism.
I did not find the discussion of ‚the rich get richer' very helpful because network theory at this stage deals only with static geometry, not with empirically-based dynamics. In fact, the dynamics of financial markets have been described empirically accurately without using any notion of networking. In the text the phrase „economic stability" is used but stability is a dynamic idea, and there is no known empirical evidence from the analysis of real markets for any kind of stability. The absence of dynamics on networks means that complexity is not described at all: there is nothing complex about the geometry of a static network! Suggesting that cell biology can be described by networking is empty so long as dynamics are not deduced from empirics. Nonempirical models of dynamics will probably not be of much use for making advances in understanding or treating cancer, e.g. Everything we know about cell biology and cancer was discovered via reductionism, by isolating cause and effect the way that a good auto mechanic does in order to repair a car.
Unfortunately, the author lets his enthusiasm get the best of him when he proclaims „laws of self-organization" and the need to go beyond reductionism. First, there are no known laws of „self-organization". The only known laws of nature are the laws of physics and consequences deduced from the laws, namely, chemistry and cell biology. Worse, every mathematical model that can be written down is a form of reductionism. Quantum theory reduces phenomena to (explains phenomena via) atoms and molecules. All of chemistry is about that. Cell biology attempts to reduce observed phenomena to DNA, proteins, and cells. Believers in self-organized criticality try to reduce the important features of nature to the equivalent of sandpiles. Network enthusiasts hope to reduce phenomena to nodes and links. In order to try to isolate cause and effect, there is no escape from reductionism of one form or another, holism being an empty illusion. So I did not at all like the assertion on pg. 200 that globalization (via deregulation and privatization) is inevitable, because there is no law that tells us that it is.
Summarizng: there is no complexity without dynamics, there are no known „laws of self-organization", and reductionism is the only hope for doing science. Anyone who disagrees with this is welcome to explain to me and others the alternative (jmccauley@uh.edu).