Abstract
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.
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