by Duncan J. Watts
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Book Description
The pioneering young scientist whose work on the structure of small worlds has triggered an avalanche of interest in networks. In this remarkable book, Duncan Watts, one of the principal architects of network theory, sets out to explain the innovative research that he and other scientists are spearheading to create a blueprint of our connected planet. Whether they bind computers, economies, or terrorist organizations, networks are everywhere in the real world, yet only recently have scientists attempted to explain their mysterious workings. From epidemics of disease to outbreaks of market madness, from people searching for information to firms surviving crisis and change, from the structure of personal relationships to the technological and social choices of entire societies, Watts weaves together a network of discoveries across an array of disciplines to tell the story of an explosive new field of knowledge, the people who are building it, and his own peculiar path in forging this new science. 24 b/w illustrations.
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You may be only six degrees away from Kevin Bacon, but would he let you borrow his car? It depends on the structures within the network that links you. When the power goes out, when we find that a stranger knows someone we know, when dot-com stocks soar in price, networks are evident. In Six Degrees, sociologist Duncan Watts examines networks like these: what they are, how they're being studied, and what we can use them for. To illustrate the often complicated mathematics that describe such structures, Watts uses plenty of examples from life, without which this book would quickly move beyond a general science readership. Small chapters make each thought-provoking conclusion easy to swallow, though some are hard to digest. For instance, in a short bit on "coercive externalities," Watts sums up sociological research showing that: "Conversations concerning politics displayed a consistent pattern .... On election day, the strongest predictor of electoral success was not which party an individual privately supported but which party he or she expected would win." Six Degrees attempts to help readers understand the new and exciting field of networks and complexity. While considerably more demanding than a general book like The Tipping Point, it offers readers a snapshot of a riveting moment in science, when understanding things like disease epidemics and the stock market seems almost within our reach. --Therese Littleton
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Average Customer Review:
0 of 0 people found the following review helpful:
 Real-world networks are the result of nonrandom structure, 2007-08-12
Random Graph Theory: Image throwing a box full of buttons on a table and then choosing a pair of buttons at random and connect them with a piece of string. What would the buttons look like over a period of time. "In particular, what features could we prove that all such networks must have?" If you pickup one of the buttons what would be its connected component? "The fraction of the nodes connected in a single component change suddenly when the average number of links per node exceeds one." If we add enough thread so each button has one thread the fraction of the graph that occupied by the largest component suddenly jumps from almost zero to one. A phase transition from unconnected to connected and the point this happens is called the critical point. "Phase transitions of one sort or another occur in many complex systems and have been used to explain phenomena as diver as the onset of magnetization, the explosion of disease epidemics, and the propagation of fads. In the particular case, the phase transition is driven by the addition of a small number of links right near the critical point that have the effect of connecting many very small clusters into a single giant component, which then proceeds to swallow up all the other nodes until everything is connected." "So the presence of a giant component means that whatever happens at one location in the network has the potential to affect any other location." "The line between isolation and connectedness is thus an important threshold for the flow of information, disease, money, innovations, fads, social norms, and pretty much everything else that we care about in the moder society. The global connectivity should arrive not incrementally but in a sudden, dramatic jump tells us something deep and mysterious about the world." Almost everything we know about complex networks tells us that "they are not random." "Nevertheless, if we would like to understand the properties and behavior of real-world networks, the issue of nonrandom structure is one that eventually has to be faced."
4 of 5 people found the following review helpful:
Opens up the world, 2007-04-05
We used this book in a doctoral seminar addressing shifting practices of "meaning making" in a networked society. It was the one book that everyone agreed was outstanding in all areas: aside from the depth and level of scholarship in Watts's work, he also has an extremely approachable style, one that will make the book useful to scholars and laymen alike.
0 of 3 people found the following review helpful:
Efficient and Excellent!!!, 2007-03-10
No more other words to say, I am really satisfied with the service!
11 of 13 people found the following review helpful:
Excellent for its audience, 2006-04-30
I wrote this book review as an assignment for a class. Its intended audience was sociologists unfamiliar with network theory. The intended audience for the book though is much wider. If you want the math, read academic journals.
In the first chapter of Six Degrees Duncan Watts notes that gossip, power outages, epidemics, even properties of the human brain such as consciousness are phenomena that may be understood as emerging from the interaction of their constituent elements. Through such examples, he calls attention to the broad applicability of his subject matter. Having provided this motivation, Watts spends much of first half of the book discussing what he knows best, "small world" networks. In the second half he presents a network perspective for a wide range of topics such as epidemics, externalities, speculation, social decision making, and organizations.
Like many academics marketing books to non-academics, Watts skillfully weaves his personal story with the science. His personal story is not only provided to keep laymen interested. Watts is now a member of the sociology department at Columbia University, but one can't help but wonder whether he identifies as a sociologist? How would other members of the discipline respond to a youngster whose PhD is in theoretical and applied mechanics who may never have read Durkheim? His early collaborators were mathematicians, physicists, and computer scientists lodged in appropriate departments. Watts though, has become a strong proponent of interdisciplinary science, and he respectfully acknowledges research that has been done in anthropology, sociology, psychology and economics.
His first foray in the social sciences was inspired by the "small world" phenomenon. When two people are surprised to learn they have mutual acquaintances, someone often says, "It's a small world." In 1967, social psychologist Stanley Milgram decided to investigate how small the world really is. He tasked randomly selected residents of Boston and Omaha with getting a letter to a stockbroker who lived in Massachusetts. The rule was, they could only send the letter to people they knew on a first name basis. Amazingly, the letters that reached their destination usually did it in just 6 steps. This finding was then misconstrued and became the urban legend that there are six degrees of separation between any two people. Despite the widespread interest in the small world phenomena, little progress was made understanding it over the next thirty years.
Watts got interested in this problem when he was a graduate student in theoretical and applied mechanics. He and his advisor, Steven Strogatz, had been trying to understand how crickets' chirping becomes synchronized without a conductor cricket. Watts surmised that the timing of a cricket's chirp must be influenced by where it is located and the other crickets it is listening to. The ability to synchronize may depend on the structure of this network of crickets. The relationship between network structure and network phenomena such as synchronicity suddenly seemed broadly important, and he was surprised to learn how little mathematical attention it had garnered. Recalling the idea of "six degrees of separation," Watts and Strogatz turned to social networks and set about building simple models. Where Milgram had asked, "How small is the world?" they were now asking, "What does it take to make a world small?" This reframing of the problem was fundamental to the contribution they were to make.
Watts and Strogatz settled on modeling just two facets of social networks. One was the "small world" aspect, quantified as average path length (the number of links required to connect two randomly chosen people). The second was clustering, the extent to which my friends overlap with my friends' friends. What makes small world networks surprising is that short path lengths and high clustering are inherently antagonistic. Paul Erd?s and Alfred R?nyi rigorously proved that path lengths are short in networks with no inclination towards increased clustering, a random graph in the parlance of mathematicians. At the opposite extreme, if everyone was friends with all of their friends' friends, short path lengths would be impossible (in fact social groups would be completely disconnected from each other). After countless computer simulations, Watts had two important results. The alpha model captured the small world balance of path length and clustering. The beta model showed that if a network was systematically clustered, to the point of fragmentation, just adding five random links (edges) halves the average path length. He then began acquiring and examining network data sets. Remarkably, Hollywood actor collaborations, the neurology of C. Elegans, the power grid of the Western United States, interlocking boards of directors and the world wide web are all small world networks.
Next Watts reviews the work by L?zl? Barab?si, a physicist at the University of Notre Dame. His major contribution is research on scale free networks. Sociologists have long been concerned with questions surrounding the number of connections (degree) people have. Barab?si realized the importance of the degree distribution in a network. The degree distribution of many networks is approximately Poisson but Barabasi showed that the degree distribution of other important networks follows the highly skewed power-law. The distribution of wealth and the size of cities both fit this model. Furthermore he showed that this distribution will follow if the future growth rate is linearly related to the present size. This has obvious implications for these two examples and calls to mind Merton's Matthew Effect.
Barab?si's book, Linked, is similar to Six Degrees in that is geared to the general public and reviews many of the most important advances in network scholarship. Do Watts and Barab?si overstate their case? Rather than get bogged down in the semantic debate that is likely to arise from the claim to a "new" science, we should appraise the value of this line of research. It clearly has potential but Watts himself sometimes alludes to the difficulties in achieving that potential. Watts' work is mostly theoretical. Six Degrees offers a thought provoking network perspective on many topics but little help harnessing the theory in empirical work. Appropriate data may be hard to come by. Perhaps Watts has provided ideas that creative empiricists will find ways to exploit, but there are methodological challenges that may prove to be stubborn.
Despite some important exceptions such as Granovetter's Strength of Weak Ties sociologists have tended to take one of two approaches. One was to focus on the relationship between social structure and network structure. The other was to view network ties as sources of information or influence. This means exploring the association between position in a network, and a node's identity or power. Watts is right to call attention to the fact that these approaches usually ignored dynamics: changes in the network structure (changes in network connections), and what individuals do on the network (search for information, spread rumors, make decisions). Network data that captures these dynamics may be harder to come by.
Furthermore, large detailed datasets may be limited by the computational power available. Even simple computer simulations can be very computationally demanding. Threshold models of decision making, discontinuous phase transitions and cascades - many of the fundamental concepts in the study of networks are nonlinear. Proving the existence of causal relationships is always a challenge but these complex systems make a hash of everything. The measured effect of an independent variable, on average or at the margin, tells us little about the importance of that variable.
Despite a reasonable display of humility and respect, Watts should be criticized for the sociology he leaves out. Neither space limitations, nor a rush to publication can justify the gaps in his otherwise helpful recommendations for further reading. For example, Blau, Burt, Coleman, Homans, Laumann, Marwell and Oliver are conspicuously absent from the list. Perhaps this observation should not be overanalyzed but it does brings us back to how Watts will be received by sociologists and what impact he and scholars outside the discipline will have on sociology. It is hard for this reviewer to understand how anyone who reads this book could come away uncertain of the value of mathematics for theory development as well as empirical analysis. Model building can simplify and clarify, enhancing our intuition. Watts would never argue that all sociologists should drop what they're doing and begin running computer simulations, just that we should be open to such approaches. As he points out, "For any complex system, there are many simple models we can invent to understand its behavior. The trick is to pick the right one. And that requires us to think carefully, to know something about the essence of the real thing." Sociologists know something about the real thing. That's why we can't leave all the modeling to physicists and economists.
5 of 7 people found the following review helpful:
"Six Degrees" - A Reaction to Professor Watts' Seminal Work, 2006-01-13
The book is not a user's guide to social networking. This is not "Networking for Dummies"! It is a thoughtful treatment by an academic of a fascinating topic - or to be more precise - an intriguing network of interrelated topics.
In presenting the material in his book, Dr. Watts tells two stories in parallel. At one level, he describes the evolution of his work and that of his colleagues in trying to solve the problem of modeling and understanding the dynamics within a wide variety of types of networks. The networks described include electric power grids, social networks, AIDS and Ebola virus epidemics, hierarchical organizational charts in Fortune 500 firms and financial markets. At another level, Watts uses the story of the arc of his research as a case study to describe the emergence of a whole new branch of science: the science of networks. In one sense, as I made my way through the ten chapters of this book, I felt I had been invited into a microbiology laboratory to view the results of experiments in which Watts and his gifted colleagues has served as human Petri dishes that had hosted the incubation of germs of ideas that had been cultured from a wide variety of disciplines and streams of thought.
As a recruiter and an avid practitioner of social networking, I found much to ponder in these chapters. Chapter 5, "Search in Networks," is particularly relevant to the problem of how best to think about finding the right person via directed searches or broadcast searches. I also found enlightening Watt's tracing of the development of the popular concept of "Six Degrees of Separation" from its inception in 1967 the research of social psychologist Stanley Milgram into the "small-world problem." through its current level of cachet in popular parlance.
As a Renaissance Soul who believes firmly in the value of helping companies to discover and to hire broadly educated leaders, I was particularly encouraged by Chapter 9, "Innovation, Adaptation, and Recovery." Standing on the shoulders of two MIT professors, Chuck Sabel and Michael Piore, whose 1984 book, The Second Industrial Divide, warned of a sea change in industrial organization, Watts surveys the challenges of organizational structure and communication in an age of ambiguity. Implicit throughout this book is a point that he makes explicit in this chapter: the only way to function effectively in this world of growing complexity and ambiguity is to utilize strategies of collaboration across traditional boundaries. This principle is true in facing the challenges of creating a new science of networking. Boundaries had to be crossed and chasms bridged that had traditionally separated scientists in their own fiefdoms of physics, economics, mathematics, sociology in order to be able to begin to model network behaviors and dynamics. I see the same dynamics at work in the nascent field of nanotechnology, in which biologists, physicists, material scientists, electrical engineers, optics specialists and software engineers are all working together to solve problems and grasp emerging opportunities.
In much the same way, the only reasonable approach to resolving complex challenges within organizations is to create collaboration strategies that connect individual and teams that traditional have done their work in isolation from one another. As a compelling case in point, Watts dissects the Toyota-Aisin crisis of 1997 and its stunning resolution.
I am more convinced than ever before that the challenges of complexity and ambiguity in the world of business will be faced most successfully by companies that have the vision to hire as leaders Renaissance Men and Women who understand at the very core of their being the value and power of collaboration across traditional boundaries of thought, academic discipline and functional role within an organization.
I am grateful to Dr. Watts for taking his experience from academic work and making it applicable and accessible to those of use practicing outside the world of academia.
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