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Abstract
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Brain, as a self-organized critical system, is the most complex system in nature, and has been always attractive for many scientists. Brain functionality depends on various features, the most important of which is the topological structure of the neuronal network. Several research studies found that the small-world property has a substantial impact on optimizing the brain function. But this is still a questionable finding, which necessitates more investigation for better understanding of the brain complex network. In this study, we investigate the importance of the effect of high connectivity on the brain network, and also on its self-organization property. In this respect, we simulate the brain structure using complex network theory, and using a spreading model for the brain dynamics. We also investigate the effect of heterogeneity of the connectivity by generating different types of networks, such as Erdos-Renyi, Small-World and Scale-Free networks. We show that by increasing the average degree, the avalanche size/duration distributions approach into the universal critical power-law behavior with mean-field solutions, independent of the network topology. On the other hand, we also show that for a network with small average degree, in spite of possessing the small-world property, the system is far from the critical state. We conclude that one of the most important factors affecting the performance of self-organization of the brain may be high connectivity, which is in agreement with the observations.
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