Preferential interaction networks: A dynamic model for brain synchronization networks

In this work, we propose a weighted network model called a preferential interaction network (PIN), whose construction is based on mechanisms similar to those of the scale-free network model developed by Albert and Barabási. The PIN aims to reproduce the behaviour of real systems of fixed size in which stronger connections are reinforced over time. Its composition starts with a network with fixed nodes, and obeys two basic processes: firstly, an increase in the edge weights, and secondly, a preferential interaction is added. Preferential interaction is defined as the tendency whereby edges with larger weights are more likely to be chosen in a iteration. PIN has three parameters: the size of the network, the rate of increase of the weights, and the number of iterations. These parameters were used to fit the model to EEG brain synchronization networks of healthy subjects. The complementary cumulative distribution of weight in the model was compared to the corresponded distribution in EEG networks. The shape of the model distribution showed similar to those of the EEG data networks and the PIN model topology index are closer than a random null model, suggesting that a preferential interaction process represents the core of brain synchronization dynamics.