Emergence of Scale-free Spike Flow Graphs in Recurrent Neural Networks

In recent two decades neuroscience and computational intelligence has experienced a large progress, with some new important concepts being developed like spiking (Bohte, 2003) and dynamical neurons (Izhikevich, 2006). Due to increase in computational power available for researchers, many impressive simulations have been carried out and some other ones are yet to come. These developments in CI have occurred simultaneously with some very interesting theoretical and empirical results in random graph theory - the introduction of small-world (Watts and Strogatz, 1998) and scale-free (Barabasi and Albert, 1999), (Albert and Barabasi, 2002) models, and investigation of their properties. Based on results already published by other authors (Davey et al., 2004), (Kwok et al., 2006) we believe that the edge of these two dynamically growing disciplines might be an interesting field for research. In this paper we introduce a simplified model of spike flow network which in some details resembles a recurrent neural network with stochastic dynamics. We argue that within this setup a scale-free network structure emerges as a natural consequence of model structuring principles and we provide numerical evidence supporting this claim. Further in the paper we investigate a number of interesting properties of this network and discuss some consequences of this result