{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T17:12:34Z","timestamp":1770743554249,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,30]],"date-time":"2019-01-30T00:00:00Z","timestamp":1548806400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["HO4695\/3-1"],"award-info":[{"award-number":["HO4695\/3-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>With the aim of further advancing the understanding of the human brain\u2019s 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.<\/jats:p>","DOI":"10.3390\/e21020128","type":"journal-article","created":{"date-parts":[[2019,1,30]],"date-time":"2019-01-30T10:58:27Z","timestamp":1548845907000},"page":"128","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Characterizing Complex Networks Using Entropy-Degree Diagrams: Unveiling Changes in Functional Brain Connectivity Induced by Ayahuasca"],"prefix":"10.3390","volume":"21","author":[{"given":"Aline","family":"Viol","sequence":"first","affiliation":[{"name":"Institute of Theoretical Physics, Technische Universit\u00e4t Berlin, Hardenbergstra\u00dfe 36, 10623 Berlin, Germany"},{"name":"Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universit\u00e4t zu Berlin, Philippstra\u00dfe 13, 10115 Berlin, Germany"}]},{"given":"Fernanda","family":"Palhano-Fontes","sequence":"additional","affiliation":[{"name":"Brain Institute, Universidade Federal do Rio Grande do Norte, Natal\u2013RN 59078-970, Brazil"}]},{"given":"Heloisa","family":"Onias","sequence":"additional","affiliation":[{"name":"Brain Institute, Universidade Federal do Rio Grande do Norte, Natal\u2013RN 59078-970, Brazil"}]},{"given":"Draulio B.","family":"de Araujo","sequence":"additional","affiliation":[{"name":"Brain Institute, Universidade Federal do Rio Grande do Norte, Natal\u2013RN 59078-970, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1370-4272","authenticated-orcid":false,"given":"Philipp","family":"H\u00f6vel","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics, Technische Universit\u00e4t Berlin, Hardenbergstra\u00dfe 36, 10623 Berlin, Germany"},{"name":"Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universit\u00e4t zu Berlin, Philippstra\u00dfe 13, 10115 Berlin, Germany"},{"name":"School of Mathematical Sciences, University College Cork, Western Road, T12 XF62 Cork, Ireland"}]},{"given":"Gandhi M.","family":"Viswanathan","sequence":"additional","affiliation":[{"name":"Department of Physics, Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil"},{"name":"National Institute of Science and Technology of Complex Systems Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1038\/nn.4502","article-title":"Network neuroscience","volume":"20","author":"Bassett","year":"2017","journal-title":"Nat. Neurosci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1093\/comnet\/cnt006","article-title":"Cascading behaviour in complex socio-technical networks","volume":"1","author":"Moreno","year":"2013","journal-title":"J. Complex Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"0101","DOI":"10.1038\/s41559-017-0101","article-title":"The multilayer nature of ecological networks","volume":"1","author":"Pilosof","year":"2017","journal-title":"Nat. Ecol. Evol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1038\/nrn1931","article-title":"Decoding mental states from brain activity in humans","volume":"7","author":"Haynes","year":"2006","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.socnet.2004.11.009","article-title":"A measure of betweenness centrality based on random walks","volume":"27","author":"Newman","year":"2005","journal-title":"Soc. Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1016\/j.tics.2013.09.012","article-title":"Network hubs in the human brain","volume":"17","author":"Sporns","year":"2013","journal-title":"Trends Cogn. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4012","DOI":"10.1016\/j.physa.2012.02.033","article-title":"Identifying all-around nodes for spreading dynamics in complex networks","volume":"391","author":"Hou","year":"2012","journal-title":"Physica A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1124\/jpet.103.049882","article-title":"Human Pharmacology of Ayahuasca: Subjective and Cardiovascular Effects, Monoamine Metabolite Excretion, and Pharmacokinetics","volume":"306","author":"Riba","year":"2003","journal-title":"J. Pharmacol. Exp. Ther."},{"key":"ref_10","unstructured":"Hofmann, A., Ott, J., and Feilding, A. (2013). LSD: My Problem Child, OUP Oxford."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1111\/j.1755-5949.2008.00059.x","article-title":"The Pharmacology of Lysergic Acid Diethylamide: A Review","volume":"14","author":"Passie","year":"2018","journal-title":"CNS Neurosci. Ther."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Shanon, B. (2002). The Antipodes of the Mind: Charting the Phenomenology of the Ayahuasca Experience, Oxford University Press.","DOI":"10.1093\/oso\/9780199252923.001.0001"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Labate, B.C., and Cavnar, C. (2014). Ayahuasca Shamanism in the Amazon and Beyond, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199341191.001.0001"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Labate, B.C., and Cavnar, C. (2014). Prohibition, Religious Freedom, and Human Rights: Regulating Traditional Drug Use, Springer.","DOI":"10.1007\/978-3-642-40957-8"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Labate, B.C., and Cavnar, C. (2013). The Therapeutic Use of Ayahuasca, Springer.","DOI":"10.1007\/978-3-642-40426-9"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s002130000606","article-title":"Subjective effects and tolerability of the South American psychoactive beverage Ayahuasca in healthy volunteers","volume":"154","author":"Riba","year":"2001","journal-title":"Psychopharmacology"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Shanon, B. (2002). Antipodes of the Mind, Oxford University Press.","DOI":"10.1093\/oso\/9780199252923.001.0001"},{"key":"ref_18","unstructured":"Newman, M.E.J. (2010). Networks: An Introduction, Oxford University Press, Inc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1103\/RevModPhys.74.47","article-title":"Statistical mechanics of complex networks","volume":"74","author":"Albert","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1016\/j.neuroimage.2009.10.003","article-title":"Complex network measures of brain connectivity: Uses and interpretations","volume":"52","author":"Rubinov","year":"2010","journal-title":"NeuroImage"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2019small-world\u2019 networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7388","DOI":"10.1038\/s41598-017-06854-0","article-title":"Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca","volume":"7","author":"Viol","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1126\/science.1065103","article-title":"Specificity and Stability in Topology of Protein Networks","volume":"296","author":"Maslov","year":"2002","journal-title":"Science"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/TCNS.2014.2357551","article-title":"Pattern Synchronization of Nonlinear Heterogeneous Multiagent Networks With Jointly Connected Topologies","volume":"1","author":"Chen","year":"2014","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Stella, M., and De Domenico, M. (2018). Distance Entropy Cartography Characterises Centrality in Complex Networks. Entropy, 20.","DOI":"10.3390\/e20040268"},{"key":"ref_26","first-page":"20","article-title":"The entropic brain: A theory of conscious states informed by neuroimaging research with psychedelic drugs","volume":"8","author":"Leech","year":"2014","journal-title":"Front. Hum. Neurosci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"423","DOI":"10.3389\/fnhum.2016.00423","article-title":"Commentary: The entropic brain: a theory of conscious states informed by neuroimaging research with psychedelic drugs","volume":"10","author":"Papo","year":"2016","journal-title":"Front. Hum. Neurosci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.neuropharm.2018.03.010","article-title":"The entropic brain\u2014Revisited","volume":"142","year":"2018","journal-title":"Neuropharmacology"},{"key":"ref_29","unstructured":"Association, A.P., and DSM-IV-TR, American Psychiatric Association (2000). Diagnostic and Statistical Manual of Mental Disorders: DSM-IV-TR. Diagnostic and Statistical Manual of Mental Disorders, American Psychiatric Association Publishing."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2550","DOI":"10.1002\/hbm.21381","article-title":"Seeing with the eyes shut: Neural basis of enhanced imagery following ayahuasca ingestion","volume":"33","author":"Ribeiro","year":"2012","journal-title":"Hum. Brain Mapp."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1002\/hbm.20113","article-title":"Spontaneous low-frequency BOLD signal fluctuations: An fMRI investigation of the resting-state default mode of brain function hypothesis","volume":"26","author":"Fransson","year":"2005","journal-title":"Hum. Brain Mapp."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.yebeh.2013.11.019","article-title":"Brain complex network analysis by means of resting state fMRI and graph analysis: Will it be helpful in clinical epilepsy?","volume":"38","author":"Onias","year":"2014","journal-title":"Epilepsy Behav."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"12832","DOI":"10.1523\/JNEUROSCI.6046-11.2012","article-title":"Spatiotemporal Reconfiguration of Large-Scale Brain Functional Networks during Propofol-Induced Loss of Consciousness","volume":"32","author":"Schroter","year":"2012","journal-title":"J. Neurosci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1093\/brain\/awn018","article-title":"Disrupted small-world networks in schizophrenia","volume":"131","author":"Liu","year":"2008","journal-title":"Brain"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/128\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:29:43Z","timestamp":1760185783000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/128"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,30]]},"references-count":34,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["e21020128"],"URL":"https:\/\/doi.org\/10.3390\/e21020128","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,30]]}}}