Nexus by Mark Buchanan
Posted on July 28th, 2005
I read this book back in June right after On Intelligence and never got around to posting my comments about it. I think I'll just do my usual and post quotes that I found especially interesting.
I will say that Nexus was by far one of the best books I've read networks. There's a bit of content overlap between this book and Albert-Laszlo Barabasi's book Linked, but plenty of new material as well.
p. 40
The psychologist Carl Jung once speculated about the existence of what he termed the "collective unconscious", a web of archaic psychological connections between people of which we are normally not aware. In Jung's view, these hidden interpersonal connections might account for all manner of strange coincidences, as when a person wakes at 4 A.M. with a start and later discovers that this was the very moment when a loved one died many thousands of miles away.
p. 42
The crucial links, as Granovetter went on to show, are the weak links between people, especially those that he called social "bridges."
p. 46
... This is Granovetter's basic insight: the crucial importance in the social fabric of bridging links between weak acquaintances. Without weak ties, a community would be fragmented into a number of isolated cliques.
p. 55
...the long-distance social shortcuts that make the world small are mostly invisible in our ordinary social lives. We can only see as far as those to whom we are directly linked-- by strong or weak ties alike. We do not know all the people our friends know, let along the friends and acquaintances of those people. It stands to reason that the shortcuts of the social world lie mostly beyond our vision, and only come into our vision when we stumble over their startling consquences.
p. 86
The Internet and the World Wide Web do not quite fit Watts and Strogatz's pattern but rather achieve the same small-world end in a different way-- by having a few elements with a huge number of links. In other words, there is more than one way for a network to be a small world, or, put another way, there is more to say about a network than that it is or is not a small world. If Watts and Strogatz's discovery was a first step into the world of disorderly and complex networks, then the recognition of the importance of hubs and the power-law pattern for the distribution of links is the second. And what's more, the emergence of hubs is by no means a curiosity of man-made information networks such as the Internet and the World Wide Web.
p. 88
Oddly enough, the small-world architecture even turns up in the structure of human language. Last year physicists Ricard Sole and Ramon Ferrer i Cancho used the database of the British National Corpus, a 100-million-word collection of samples of written and spoken language from a wide range of sources, to study the grammatical relationships between 460,902 words in the English language. they considered two words to be "linked" if they appear next to one another in English sentences. Once again, everything tumbled out just as for the other networks. A handful of words were extremely well-connected hubs, frequently appearing next to any of a huge number of other words. Words such as a, the, or at work as hubs of this sort. The typical "distance" between words in the language was less than three, just about what you would expect for a language of the same number of words that was put together at random. Nevertheless, the clustering of the network was nearly five thousand times higher than for a random network, revealing that words fall into cliques and groups, as do people within social networks. The English language is another small-world network.
Ref: Ramon Ferrer i Cancho and Ricard V. Sole, "The Small World of Human Language," working paper 01-03-016, Sante Fe Institute, Sante Fe, N.M., 2001
p. 103
The real importance of the power law is that it reveals how, even in a historical process influenced by random chance, law-like patterns can still emerge. In terms of their self-similar nature, all river networks are alike. History and chance are fully compatible with the existence of lawlike order and pattern.
p. 119
In terms of the way links get shared among the elements of a network, networks of the Watts and Strogatz variety are "egalitarian," as the links are distributed more or less equally. In contrast, highly connected hubs or connectors dominate the networks of Albert and Barabasi. The historical mechanism of the rich getting richer leads without fail to connectors, who, by virtue of having so many links, naturally play a role similar to that of Granovetter's bridges. They have a more complex form that simple long-distance links, but nonetheless bring together regions of a network that would otherwise be quite distant. In striking contrast to small-world networks of the egalitarian kind, these networks with hubs might be better described as "aristocratic," as only a handful of elements possess most of the network's links.
So there are, it seems, two flavors of small: egalitarian networks in which all the elements have roughly the same number of links and aristocratic networks characterized by spectacular disparity.
p. 125
Like the aristocratic networks of the World Wide Web or the Internet, small-world networks of the egalitarian kind can emerge from a simple process of history and growth. Whenever limitations or costs eventually come into play to impede the richest getting still richer, then a small-world network becomes more egalitarian, as seems to be the case with the airports and a number of other real-world networks.
p. 131
Random networks, despite their redundancy, fall apart quickly in the face of an uncoordinated attack.
... Since an uncoordinated attack targets elements at random, it almost always knocks out unimportant elements with few links, while missing the hubs. In this way, the small-world architecture makes a network resilient against random failure or unsophisticated attack. This finding presumably explains why the Internet, despite the continual failure of routers and other hardware elements, never collapses as a whole... As it turns out, the very feature that makes a small-world network safe from random failure could be its Achilles' heel in the face of an intelligent assault.
p. 160
Twenty-five years ago, the evolutionary biologist Richard Dawkins suggested that there might be a genetic element to the logic of spreading ideas. Just as genes pass from generation to generation, Dawkins suggested that ideas-- he called them "memes"-- may do the same: "Examples of memes are tunes, disease, catch-phrases, clothes fashions, way of making pots or building arches.."
p. 181
It seems that for diseases trying to spread in an aristocratic network, there simply is no tipping point. Diseases are always tipped and can spread no matter what.
This conclusion is weird, but the mathematics bears it out.
p. 199
Granovetter points out that in any organization or in a family or group of friends, relationships established over a time can also be the source of behavior with economic consequences. Only rarely do individuals act as isolated beings, able to pointedly pursue their own personal agenda; more frequently, we act within the context of numerous other goals and constraints originating in our social life. Any many of these goals and constraints have little to do with economic ends, but more to do with conforming to a set of shared norms and ethical values.
p. 207
So the small-world network, in the social case, seems to be a beneficial mix of both clustering and weak links that tie distinct clusters together. Clustering makes for a dense social fabric and allows the formation of social capital, which in turn helps to promote efficiency in decision making. At the same time, weak ties keep everyone close in a social sense to the rest of the community, even if it is very large, which enables each person access to the diverse information and assets of the larger organization. Perhaps organizations and communities should purposefully be built among small-world lines.
Indeed, it begins to seem as if the small-world idea is struggling to express some still deeper insight about how to live in a complex world. At its core lies the idea that too much order and familiarity is just as bad as too much disorder and novelty. We instead need to strike some delicate balance between the two.