Everyone knows the small-world phenomenon: soon after meeting a
stranger, we are surprised to discover that we have a mutual friend, or
we are connected through a short chain of acquaintances. In his book,
Duncan Watts uses this intriguing phenomenon--colloquially called "six
degrees of separation"--as a prelude to a more general exploration:
under what conditions can a small world arise in any kind of network?
The networks of this story are everywhere: the brain is a network of
neurons; organisations are people networks; the global economy is a
network of national economies, which are networks of markets, which are
in turn networks of interacting producers and consumers. Food webs,
ecosystems, and the Internet can all be represented as networks, as can
strategies for solving a problem, topics in a conversation, and even
words in a language. Many of these networks, the author claims, will
turn out to be small worlds.
How do such networks matter? Simply put, local actions can have global
consequences, and the relationship between local and global dynamics
depends critically on the network's structure. Watts illustrates the
subtleties of this relationship using a variety of simple models---the
spread of infectious disease through a structured population; the
evolution of cooperation in game theory; the computational capacity of
cellular automata; and the sychronisation of coupled phase-oscillators.
Watts's novel approach is relevant to many problems that deal with
network connectivity and complex systems' behaviour in general: How do
diseases (or rumours) spread through social networks? How does
cooperation evolve in large groups? How do cascading failures propagate
through large power grids, or financial systems? What is the most
efficient architecture for an organisation, or for a communications
network? This fascinating exploration will be fruitful in a remarkable
variety of fields, including physics and mathematics, as well as
sociology, economics, and biology.
