Emergence of scale-free properties in Hebbian networks

The fundamental `plasticity' of the nervous system (i.e high adaptability at different structural levels) is primarily based on Hebbian learning mechanisms that modify the synaptic connections. The modifications rely on neural activity and assign a special dynamic behavior to the neural networks. Another striking feature of the nervous system is that spike based information transmission, which is supposed to be robust against noise, is noisy in itself: the variance of the spiking of the individual neurons is surprisingly large which may deteriorate the adequate functioning of the Hebbian mechanisms. In this paper we focus on networks in which Hebbian-like adaptation is induced only by external random noise and study spike-timing dependent synaptic plasticity. We show that such `HebbNets' are able to develop a broad range of network structures, including scale-free small-world networks. The development of such network structures may provide an explanation of the role of noise and its interplay with Hebbian plasticity. We also argue that this model can be seen as a unification of the famous Watts-Strogatz and preferential attachment models of small-world nets.