Researchers from the Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany and collaborators have developed a model to test the speed of synchronization of complex networks.

The researchers tested this model using three very different oscillators acting on complex networks: the Kuramoto, Rössler, and pulse-coupled oscillators. As a result, for all tested networks, they showed that the structure of the coupling between network nodes determines the speed of synchronization.

The researchers found that the higher the disorder in the network, the faster the synchronization. They subsequently verified this observation in real-life networks including an air-transported network, a social network, and a human travel network.

The researchers are currently working on deriving a mathematical formula that integrates network size, the typical number of links per node, and the spread of the disorder introduced. This work could have real-life applications, for example, in measuring the robustness of the relaxation process in gene regulatory networks, the researchers said.

These models will be interesting to compare to those related to Metcalfe’s Law.

Ref.: C. Grabow, S. Grosskinsky and M. Timme, Speed of complex network synchronization, European Physical Journal B, 2011; [DOI: 10.1140/epjb/e2011-20038-9]