Nexus: Small Worlds and the Groundbreaking Science of Networks


"As Chaos explained the science of disorder, Nexus reveals the new science of connection and the odd logic of six degrees of separation." How can geometry explain the puzzles of human behavior? In this incisive insightful work Mark Buchanan presents the fundamental principles of the emerging field of "small-worlds" theory - the idea that a hidden pattern is the key to how networks interact and exchange information, whether that network is the information highway or the firing of neurons in the brain. Mathematicians, physicists, computer
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"As Chaos explained the science of disorder, Nexus reveals the new science of connection and the odd logic of six degrees of separation." How can geometry explain the puzzles of human behavior? In this incisive insightful work Mark Buchanan presents the fundamental principles of the emerging field of "small-worlds" theory - the idea that a hidden pattern is the key to how networks interact and exchange information, whether that network is the information highway or the firing of neurons in the brain. Mathematicians, physicists, computer scientists, and social scientists are working to decipher this complex organizational system, for it may yield a blueprint of dynamic interactions within our physical as well as social worlds. Highlighting groundbreaking research behind network theory. Buchanan documents mounting support for the small-worlds idea and demonstrates its multiple applications to diverse problems - whether explaining the volatile global economy or the Human Genome Project, the spread of infectious disease or ecological damage. Nexus is an exciting introduction to the hidden geometry that weaves our lives so inextricably together.
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Editorial Reviews

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The Barnes & Noble Review
A former editor of Nature with a Ph.D. in physics, Mark Buchanan brings the new science of networks to life, one that explains spooky correlations between how we function and how other complex systems function -- from individual cells to the global Internet.

Buchanan identifies crucial features shared by networks with apparently little in common, notably the "small-world" phenomenon. (Think of "six degrees of separation," whereby you're just six links away from any other human being on earth.) This idea may explain how your brain works. In aristocratic small-world networks, certain elements maintain huge numbers of links, while most maintain far fewer. This principle describes everything from ecosystems to wealth distribution.

Relatively simple computer models are shedding surprising new light on complex systems and making intriguing -- if preliminary -- predictions. Promoting commerce will tend to level income distribution, but instabilities in investment returns lead to massive, sudden disparities. Ecosystems will weather the loss of some species, but lose the wrong species, and collapse follows almost instantly. You'll get your next job through some guy you haven't seen in years, not your best friend.

If you were fascinated by Malcolm Gladwell's The Tipping Point, read this next. Buchanan places Gladwell's ideas -- and many others -- in a broader context, showing how scientists are beginning to make sense of the crucial interactions that define our lives. (Bill Camarda)

John L. Casti
Finally, a readable, simple explanation of one of the most surprising rules of complex networks.
Library Journal
Will a network science emerge that helps us understand a variety of complex organizational systems by describing the puzzles of human behavior and connections in mathematical terms? So argues Buchanan, former editor of Nature and New Scientist. Buchanan, who holds a Ph.D. in physics, delivers a good introduction to theoretical physics and the "small worlds" theory of networks. He sees biology, computer science, physics, and sociology as intimately connected. Buchanan illustrates social and physical networks with examples ranging from the infamous "six degrees of separation" theories, to the spread of the AIDS virus, to the mapping of the nervous system of the nematode worm. Are the similarities among these networks merely a coincidence or the result of some underlying physics? Only further research will tell, but in the meantime this book is a good primer to basic network concepts and contains references to key journal articles and studies for further reading. The subject will be of particular interest to mathematicians, physicists, and computer scientists and of general interest to those in most other disciplines. Recommended for academic and larger public libraries. Colleen Cuddy, Ehrman Medical Lib., NYU Sch. of Medicine Copyright 2002 Cahners Business Information.
Kirkus Reviews
Former Nature editor Buchanan (Ubiquity, 2001) takes an intriguing, accessible look at the mathematics behind the "six degrees of separation" theory. In 1998, Cornell mathematician Duncan Watts was focused on a seemingly non-mathematical problem. In New Guinea, male fireflies by the millions perch on trees at night and flash their lights to attract females in perfect synchrony. With his advisor, Steve Strogatz, Watts was working on "graph problems," a special mathematical term describing any collection of dots connected by lines. The fireflies are the dots. Their coordinated lighting indicates information transfer, which is the equivalent of connecting lines. Watts and Strogatz's breakthrough was to see the structural similarity between the fireflies and the theory that the world's six billion people are all connected by six degrees of separation. Degrees of separation are the number of steps needed to get from one randomly selected dot to another. Watts and Strogatz showed that when networks of connected dots have a high degree of order to their clustering, the degree of separation is correspondingly high; adding random links, however, radically shrinks the degree of separation. Networks, in other words, combine order and chaos to form "small worlds." Subsequent chapters maneuver through Watts and Strogatz's work as they explain the form of the Web, the food chain, epidemiology, income distribution, and many other disparate networks. By adding the evolution of the network as a second variable, Buchanan derives two basic types of small worlds: the "aristocratic," in which the concentration of connections goes through a few "hubs"; and the egalitarian, in which connections have noparticular concentration. He suggests that small-worlds theory should change the way we think about social policy. Despite the author's penchant for distracting digressions, a terrific, essential addition to the library of popular-science books. Author tour
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Product Details

  • ISBN-13: 9780393041538
  • Publisher: Norton, W. W. & Company, Inc.
  • Publication date: 5/21/2002
  • Edition description: 1ST
  • Pages: 256
  • Product dimensions: 6.41 (w) x 9.57 (h) x 0.99 (d)

Table of Contents

Acknowledgments 9
Prelude 11
1 Strange Connections 23
2 The Strength of Weak Ties 34
3 Small Worlds 61
4 Brain Works 61
5 The Small-World Web 73
6 An Accidental Science 89
7 The Rich Get Richer 106
8 Costs and Consequences 121
9 The Tangled Web 138
10 Tipping Points 156
11 Breaking Out, Small-World Style 170
12 Laws for the Living 184
13 Beyond Coincidence 197
Notes 209
Index 223
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  • Anonymous

    Posted February 3, 2003

    A good introduction to networks

    Networks have become a very hot topic, as shown by the spate of recent books on the subject. Nexus, Mark Buchanan's recent work on "small worlds and the groundbreaking science of networks" is one of the more readable and less sensational takes on the theme. Buchanan, a physicist, science writer and editor at Nature and New Scientist, has the credentials to know what he is writing about and the ability to present it coherently. He starts with the now famous "small world" or "six degrees of separation" observation, first made in the 1960s and since studied and demonstrated in a variety of important, real-world networks. Buchanan's thesis is that physicists and mathematicians are discovering some remarkably simple laws that describe a huge number of complex systems, quite independently of the elements that make up the system. For example, The linkages that connect everyone in the world with just six steps can be treated the same way as the linkages that connect neurons in our brains or web pages on the internet. "Some of the deepest truths of our world may turn out to be truths about organization," Buchanan writes, "rather than about what kinds of things make up the world and how these things behave as individuals." Building on this theme, Buchanan systematically explores areas such as the spread of infections diseases, key social and governmental systems, brain organization, protein-based control networks within our cells, and even networks of sexual partners. Similar features, especially the "power-law" distribution, characterize all these systems. That is, whether the issue is the number of sexual partners, the number of chemical reactions, or the number of connected neurons, a few key elements account for a large percentage of the connections within each system. Buchanan shows how this grows out of a simple common dynamic characterized by the age-old observation that the rich get richer and the poor get poorer. Buchanan then goes on to trace some important implications of these emerging findings. These include the vulnerability of ecosystems to sudden collaps when a few key plants or animals are lost, the explosive transformation of a slumbering pathogen into a deadly epidemic, as seen in AIDS, and--economists and would-be-reformers take notice--the distribution of wealth. Buchanan shows that, although the exact percentages vary from country to country, the shape of the wealth-distribution curve is the same. And he demonstrates that this distribution can be shown to stem from a few extremely simple assumptions. I was struck by Buchanan's presentation of research showing that economic polices that foster business and trade, including taxation as a kind of enforced exchange, produce a flatter, more democratic distribution of wealth. On the other hand, an environment that fosters speculation inevitably transfers wealth from the poor to the rich. It turns out that the more volatile the investment markets, the more extreme that transfer. This certainly seems to match what the U.S. experienced during the savings and loan bust and the recent dot-com debacle. Those two highly speculative eras produced a lot of people riding around in limos, but also generated far more people trying to eke out a living flipping burgers. I'd very much like to see our economists and lawmakers pay attention to that finding. Nexus leaves out some important material, especially the groundbreaking work of the Santa Fe Institute. Still, it's a clear, readable and fascinating introduction to the emerging science of networks. Since we are made of networks, and embedded in them, it's hard to imagine a more relevant subject. Nexus doesn't supply the last word on this complex subject, but it's a rewarding place to start. Robert Adler, author of Science Firsts: From the Creation of Science to the Science of Creation (Wiley & Sons, September, 2002).

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