Estimation of Global and Local Complexities of Brain Networks: A Random Walks Approach

Abstract

The complexity of brain activity has been observed at many spatial scales and there exists increasing evidence supporting its use in differentiating between mental states and disorders. Here we proposed a new measure of network (global) complexity that is constructed as the sum of the complexities of its nodes (i.e, local complexity). The local complexity of each node is regarded as an index that compares the sample entropy of the time series generated by the movement of a random walker on the network resulting from removing the node and its connections, with the sample entropy of the time series obtained from a regular lattice (the ordered state) and an Erdos-Renyi network (disordered state). We studied the complexity of fMRI-based resting-state functional networks. We found that positively correlated, or \"pos\", network comprising only the positive functional connections has higher complexity than the anticorrelation (\"neg\") network (comprising the negative functional connections) and the network consisting of the absolute value of all connections (\"abs\"). We also found a significant correlation between complexity and the strength of functional connectivity. For the pos network this correlation is significantly weaker at the local scale compared to the global scale, whereas for the neg network the link is stronger at the local scale than at the global scale, but still weaker than for the pos network. Our results suggest that the pos network is related to the information processing in the brain and should be used for functional connectivity analysis instead of the abs network as is usually done.