Abstract
With the aim of further advancing the understanding of the human brain’s functional connectivity, we propose a network metric which we term the geodesic entropy. This metric quantifies the Shannon entropy of the distance distribution to a specific node from all other nodes. It allows to characterize the influence exerted on a specific node considering statistics of the overall network structure. The measurement and characterization of this structural information has the potential to greatly improve our understanding of sustained activity and other emergent behaviors in networks. We apply this method to study how the psychedelic infusion Ayahuasca affects the functional connectivity of the human brain in resting state. We show that the geodesic entropy is able to differentiate functional networks of the human brain associated with two different states of consciousness in the awaking resting state: (i) the ordinary state and (ii) a state altered by ingestion of the Ayahuasca. The functional brain networks from subjects in the altered state have, on average, a larger geodesic entropy compared to the ordinary state. Finally, we discuss why the geodesic entropy may bring even further valuable insights into the study of the human brain and other empirical networks.
Highlights
In the last few decades, new scientific fields have taken advantages of complex network approaches
The geodesic entropy is a statistical quantity that measures, in the frame of reference of a given node, the level of constraints in the aggregated influences imposed by the distribution of neighborhood radius
Functional networks are usually defined according to statistical dependencies between brain regions activities
Summary
In the last few decades, new scientific fields have taken advantages of complex network approaches. This interest emerged, in part, by virtue of technological advances that generate new datasets in computational, social, biological, and others sciences [1,2,3]. Examples include modern brain mapping techniques, such as functional magnetic resonance imaging (fMRI), that have provided previously inaccessible information about interaction patterns in the human brain [4]. The theory of complex networks has proven to be a crucial tool to understand the interactions and dynamics in large systems. Attempts to characterize new datasets bring up the challenge of extracting relevant features regarding the network’s structure. The majority of measurements that have been proposed in the last few decades allow the ranking of nodes’ importance by the number of connections, centrality, etc. [5,6,7]
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