|
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; organizations 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 synchronisation of
coupled phase-oscillators.
Watt'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.
Duncan J. Watts, who received his Ph.D.
in theoretical and applied mechanics from Cornell University
in 1997, is a postdoctoral Fellow at the Santa Fe Institute.
|
