The theory of "small-world"
networks yields insight into innumerable real-world situations, from
the Internet to the power grid, from epidemics to opinion making. A
small-world network is one where certain nodes, called hubs, have an
unusually large number of connections, so that going through hubs
one can reach any other node in just a few steps.
small-world networks, researchers have observed "critical"
thresholds -- for example, epidemics that spread uncontrollably or
spontaneously die out, depending on thresholds in the disease’s
degree of infectivity or in the number of social contacts
individuals have. But network theory has so far been poor at
modeling critical thresholds.
Now, Joseph Indekeu of Katholieke
Universiteit Leuven in Belgium (firstname.lastname@example.org) and
his colleagues have shown that small-world networks can model
critical thresholds if one tunes the hubs to be less influential on
their neighbors than the ordinary nodes. For example, a friend's
opinion could be more influential in shaping your voting preferences
than the opinion of a prominent TV commentator, whose wide audience
makes him a hub in the network. The tuning idea, the paper shows,
is mathematically equivalent to cutting off most of a hub's
connections. The authors also say their results could shed light
on, and perhaps help prevent, phenomena such as electrical blackouts
The new model even suggests a parallel between
networks and general relativity since trading in the interactions
between nodes for changes in the network's structure is reminiscent
of the gravitational interactions between bodies---gravitational
attraction---which can be mimicked by changes in the structure of
spacetime---that is, the curvature created by the presence of mass.
(Giuraniuc et al., Physical Review Letters, upcoming article)