Scale-Free Brain Networks Based on the Event-Related Potential during Visual Spatial Attention

The human brain is thought of as one of the most complex dynamical systems in the universe. The network view of the dynamical system has emerged since the discovery of scale-free networks. Brain functional networks, which represent functional associations among brain regions, are extracted by measuring the temporal correlations from electroencephalogram data. We measure the topological properties of the brain functional network, including degree distribution, average degree, clustering coefficient and the shortest path length, to compare the networks of multi-channel event-related potential activity between visual spatial attention and unattention conditions. It is found that the degree distribution of the brain functional networks under both the conditions is a power law distribution, which reflects a scale-free property. Moreover, the scaling exponent of the attention condition is significantly smaller than that of the unattention condition. However, the degree distribution of equivalent random networks does not follow the power law distribution. In addition, the clustering coefficient of these random networks is smaller than those of brain networks, and the shortest path length of these random networks is large and comparable with those of brain networks. Our results, typical of scale-free networks, indicate that the scaling exponent of brain activity could reflect different cognitive processes.