**Duncan J. Watts. Six
Degrees: The Science of a Connected Age.** New York: W.W. Norton &
Company, 2003, 368 pp., $27.95 paperback.

Review written by Phillip Bonacich, bonacich@soc.ucla.edu, University of California, Los Angeles

*Six Degrees: The Science
of a Connected Age* is a useful introduction to the impressive work
accomplished by Duncan Watts and his colleagues since Watts’ last book, *Small
**Worlds: The Dynamics of Networks
between Order and Randomness*. In *Small
Worlds,* Watts introduced sociologists to an exciting set of new
mathematical tools for the analysis of the small world phenomenon. The most
impressive part of the earlier book was its careful and productive definition
of a small world--one in which the local density of choices was high (indicating
cliquishness) but paths were short (as in a random graph). This was coupled
with the establishment of methods for continuously disturbing locally dense
graphs until they became random and the finding that density declined only
after path lengths declined, so that small worlds could exist even without
“intelligent design.” After exploring this phenomenon, Watts suggested some of
its implications for the spread of disease, evolution of cooperation, and other
network phenomena.

In his new book, Watts describes in a non-technical language the work that he and his associates have done in extending these models. Although the original papers in physics journals are worth reading, they are addressed to an audience more interested in percolation theory and Bose-Einstein condensation than in the diffusion of innovations. Watts is a bridge. The book is full of interesting and thoughtful suggestions for how these models can shed light on complex and mystifying human network behavior.

Chapters 1 through 3 review the models covered by *Small Worlds*: features of the two
apparent extremes--local solidarity and macro-level fragmentation on the one
hand and random nets with their short paths but complete lack of local
clustering on the other--can be synthesized in the form of *small world* graphs with the introduction of a few random
connections. Chapter 4 combines a shrewd criticism of Barabási’s scale-free
approach (2002) with an exposition of what Watts and his colleagues have
recently accomplished. An *affiliation network*
is a bipartite graph of people and the groups to which they belong. In a random
affiliation network all connections between individuals and groups are assigned
randomly. Watts shows that the implied networks between individuals based on
their co-memberships are small world networks--both clustered and with short
paths. Watts also shows that this model fits some data on interlocking
directorates quite well.

Chapter 5 presents some models that Watts and his colleagues have developed to study how individuals can navigate their small-world networks. The short paths available in these networks are more useful to individuals searching for jobs if the networks can be used to connect to particular others. This chapter presents two models of conditions under which these short paths can easily be found. Both models show that the searchability of networks is affected by the number of ways individuals categorize one another, and that the use of too many or too few categories impedes search. This suggests that societies with too few or too many sources of identity may both be difficult to mobilize on the basis of new identities.

Chapter 6 describes the ways in which epidemics can spread in different types of networks. Standard models of epidemiology have been developed using the well-known mathematics of random (“well-mixed”) populations. In random networks, diseases become epidemics only if infectiousness reaches a critical point; otherwise they disappear. In scale-free networks, on the other hand, there is no critical point and diseases that are not epidemics may not disappear. Hubs are easily infected and in turn infect many others. The last part of the chapter summarizes work on the vulnerability of networks of different design to failure and to attack.

Chapters 8 describes some exciting ideas about the dynamics of information cascades. Particularly interesting is Watts’ outline of the two radically different ways in which information cascades (and social movements) can fail: either through the sparseness of the network, in which case a movement will fail to diffuse because of infrequent contact, or because the network is too dense, in which case the movement fails because members are too well anchored in other relationships to be susceptible. Chapter 9 suggests a solution to the vulnerability of centralized hierarchical organizations to the loss of core members: “multiscale” networks that are “ultrarobust” with respect to failure.

Sociologists will have to adjust to Watts’ orientation to models and data, an orientation perhaps one more characteristic of physicists. His primary goal is to devise a simple but plausible model from which interesting and suggestive consequences can be drawn mathematically. There is a surprisingly casual attitude about the realism of the model--the tradeoff between fidelity and simplicity is much more in favor of the latter than we are used to. These are the features--barely plausible assumptions accepted because of their mathematical power--that many sociologists find irritating in economists: Yet, they are not irritating in this book. The reason is, I think, that Watts’ models are not dogma but are clearly tentative and under construction.

Another function of Six*
Degrees* is to make clearer the distinctive contributions of the Watts camp
and that of Albert-László Barabási, described in his recent book *Linked: The New Science of Networks*.
Barabási and his colleagues have developed the mathematics of *scale-free* networks, while Watts has
elaborated *small-world* networks. The
unbiased reader will conclude that both scale-free and small-world models are
useful under different circumstances and that both are welcome additions to our
toolkit. Small world models are appropriate when the underlying reality is one
of tightly clustered groups connected by a small number of weak ties. Ordinary
social life, in which individuals belong to tightly clustered groups of friends
and relatives supplemented by acquaintances, may be better fitted by this
model. In scale-free networks, on the other hand, geography or location within
a social space is not the primary factor determining connections. Rather,
actors wish to connect to well-connected others. Thus, the WWW, where popular
sites become even more attractive, is well suited to analysis by scale-free
networks.

Some social network researchers have faulted Watts and Barabási for ignoring previous work in the area of social networks (for example, see Pool and Kochen 1978 for an intimation of the small world model). Part of this impression may well be due to the arrogance of physicists, but I think that there is a more important reason. Their new work concerns the emergent properties of extremely large networks. Examples include the internet, collaboration networks among researchers, networks of disease spread, and large ecological networks. Until recently, data on networks of this size were not readily available. Watts’ (and Barabási’s) models will be useful to only some network researchers. They will not be useful, for example, to those who study classroom sociograms, exchange networks, organizational and individual networks in small communities, or perhaps to any researcher whose network can be printed in the pages of a journal.

We are lucky that physical scientists and mathematicians have become interested in social networks. Of course we feel slighted; not all of our contributions will be noted. But this is the cost of moving onto a very much larger intellectual stage. The mathematical tools (generating functions, percolation) are powerful. The usefulness of these models ultimately depends on social scientists with substantive interests. There are suggestive applications to a variety of phenomena, from social movements and the diffusion of information to the structure of interlocking directorates. What is needed now is the complementary expertise of other sociologists to make use of these models. The invasion of the physicists will not stop. If we are lucky they will continue to offer new mathematical and conceptual to enrich the study of social networks.

Barabási, Albert-László. 2002. *Linked: The New Science of Networks*. Cambridge, MA:

Perseus Publishing.

Pool, I. de Sola, and M. Kochen. 1978. Contacts and
Influence. *Social Networks*. 1:1-51.

Watts, Duncan J. 2003. *Six
Degrees: The Science of a Connected Age*. Cambridge, MA:

W.W. Norton.

Watts, Duncan J. 1999. *Small Worlds: The Dynamics of
Networks between Order and *

*Randomness*. Princeton, NJ:
Princeton University Press.