Controlling the Network

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In the light of recent claim of internet activities driving political events the question of how to control a network gained some importance. Controllability of Complex Networks is a paper by Yang-Yu Liu, Jean-Jacques Slotine, Albert-László Barabási. The freely available supplementary information (pdf) documents some basic terms and the research background.
Their main difference is the one of driver nodes – nodes that have the ability to change the state of the network – and hubs – nodes with many links.

For example, we show that driver nodes tend to avoid hubs, while on the contrary hubs can facilitate synchrony by providing common inputs to downstream nodes.

In order to calculate the controllability of the netwrok the authors decided to classify and weigh each link in to three di?erent types

according to its role in maintaining controllability: (1) critical if in its absence we need to increase the number of driver nodes to maintain full control of the system; (2) redundant if it can be removed without a?ecting the current set of driver nodes; (3) ordinary if it is neither critical nor redundant, i.e., its removal can
eliminate some control con?gurations, but the network can still be controllable in its absence with the same number of driver nodes.

We may look forward to see these calculation implemented in social networks. Of course, advertising as much as political agencies will pay some attention to their results.
An important question will be if the network facilitates simple structures of control or if it enables the creation of independent modes of autonomy. Beyond doubt remains the fact that the networks will be the main stage for political activities of whatever sort.