The complexity of brain activity has been observed at many spatial scales and has been proposed to differentiate between mental states and disorders. Here we introduced a new measure of (global) network complexity, constructed as the sum of the complexities of its nodes (i.e., local complexity). The complexity of each node is obtained by comparing 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 (ordered state) and a random network (disordered state). We studied the complexity of fMRI-based resting-state networks. We found that positively correlated ( pos ) networks comprising only the positive functional connections have higher complexity than anticorrelation ( neg ) networks (comprising the negative connections) and the network consisting of the absolute value of all connections ( abs ). We also observed a significant correlation between complexity and the strength of functional connectivity in the pos network. Our results suggest that the pos network is related to the information processing in the brain and that functional connectivity studies should analyze pos and neg networks separately instead of the abs network, as is commonly done. Author Summary Current measures of network complexity fail to capture the structural and functional diversity of brain networks, in which hierarchies of linked communities span across several spatial scales, from cortical minicolumns to large-scale networks. In this paper we use random walks processes to obtain a time series reflecting the complex structure of brain networks and use this time series to construct measures of local and global complexity. We found that complexity is significantly correlated to the strength of the connections in the positively correlated brain network, being stronger at the global than at the local scale.