Hierarchical modular structure enhances the robustness of self-organized criticality in neural networks

One of the most prominent architecture properties of neural networks in the brain is the hierarchical modular structure. How does the structure property constrain or improve brain function? It is thought that operating near criticality can be beneficial for brain function. Here, we find that networks with modular structure can extend the parameter region of coupling strength over which critical states are reached compared to non-modular networks. Moreover, we find that one aspect of network function-dynamical range-is highest for the same parameter region. Thus, hierarchical modularity enhances robustness of criticality as well as function. However, too much modularity constrains function by preventing the neural networks from reaching critical states, because the modular structure limits the spreading of avalanches. Our results suggest that the brain may take advantage of the hierarchical modular structure to attain criticality and enhanced function.