Estimation of global and local complexities of brain networks: A random walks approach

Abstract

<jats:p> 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. </jats:p>

Resting-state functional MRI in multicenter studies on multiple sclerosis: a report on raw data quality and functional connectivity features from the Italian Neuroimaging Network Initiative

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Signal propagation in complex networks

“…Graphs are widespread across physics (e.g., studies in quantum system [528][529][530] and non-equilibrium dynamics [531][532][533]), biology (e.g., analyses of brain [534][535][536][537][538][539], metabolic [540][541][542], and protein [543][544][545] networks), social science (e.g., scientific community [546][547][548] and opinion formation [549][550][551]), and computer science (e.g., analyses of internet [552][553][554] and information flow [555,556]), etc. Numerous challenging tasks can be addressed by studying graphs, which implies the rapid progress of graph theories [119].…”

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