Networking Can Be Critical, Literally

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.

In real-life 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 (joseph.indekeu@fys.kuleuven.be) 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 and epidemics.

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)