Characterizing Complex Networks Using Entropy-Degree Diagrams: Unveiling Changes in Functional Brain Connectivity Induced by Ayahuasca

Abstract

Open problems abound in the theory of complex networks, which has found successful application to diverse fields of science. With the aim of further advancing the understanding of the brain's functional connectivity, we propose to evaluate a network metric which we term the geodesic entropy. This entropy, in a way that can be made precise, quantifies the Shannon entropy of the distance distribution to a specific node from all other nodes. Measurements of geodesic entropy allow for the characterization of the structural information of a network that takes into account the distinct role of each node into the network topology. 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, such as self-organized criticality sometimes seen in such contexts. We apply these concepts and methods to study the effects of how the psychedelic Ayahuasca affects the functional connectivity of the human brain. We show that the geodesic entropy is able to differentiate the functional networks of the human brain in two different states of consciousness in the resting state: (i) the ordinary waking state and (ii) a state altered by ingestion of the Ayahuasca. The entropy of the nodes of brain networks from subjects under the influence of Ayahuasca diverge significantly from those of the ordinary waking state. The functional brain networks from subjects in the altered state have, on average, a larger geodesic entropy compared to the ordinary state. We conclude that geodesic entropy is a useful tool for analyzing complex networks and discuss how and why it may bring even further valuable insights into the study of the human brain and other empirical networks. * aline.viol@bccn-berlin.de †

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