Illustration of fully-connected and broken Erdős–Rényi networksThe Erdős–Rényi model could capture the occasional long-range
connections that occurred in real networks, but it couldn’t reproduce
the clustering of interactions. This discrepancy was resolved in 1998,
when mathematicians Duncan Watts and Steven Strogatz developed
the concept of a ‘small-world’ network, in which most links were local
but a few were long-range. They found that such networks cropped
up in all sorts of places: the electricity grid, neurons in worm brains,
co-stars in film casts, even Erdős’s academic collaborations.[57] It
was a remarkable finding, and more discoveries were about to follow.
The small-world idea had addressed the issue of clustering and
long-range links, but physicists Albert-László Barabási and Réka
Albert spotted something else unusual about real-life networks. From
film collaborations to the World Wide Web, they’d noticed that some
nodes in the network had a huge number of connections, far more
than typically appeared in the Erdős–Rényi or small-world networks.
In 1999, the pair proposed a simple mechanism to explain this
extreme variability in connections: new nodes that joined the network
would preferentially attach to already popular ones.[58] It was a case
of the ‘rich get richer’.
The following year, a team at the University of Stockholm showed
that the number of sexual partnerships in Sweden also appeared to