{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:37:35Z","timestamp":1760240255217,"version":"build-2065373602"},"reference-count":67,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T00:00:00Z","timestamp":1555545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["2016-75963-P"],"award-info":[{"award-number":["2016-75963-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we analyze the response times of students to yes\/no decision tasks from the perspective of network science. We analyze the properties of the natural visibility graphs (NVG) associated with their reaction time series. We observe that the degree distribution of these graphs usually fits a power-law distribution     p  ( x )  =  x  \u2212 \u03b1      . We study the range in which parameter    \u03b1    occurs and the changes of this exponent with respect to the age and gender of the students. In addition to this, we also study the links between the parameter    \u03b1    and the parameters of the ex-Gaussian distribution that best fit the response times for each subject.<\/jats:p>","DOI":"10.3390\/sym11040563","type":"journal-article","created":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T11:58:21Z","timestamp":1555588701000},"page":"563","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Power-Law Distribution of Natural Visibility Graphs from Reaction Times Series"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6371-8229","authenticated-orcid":false,"given":"Ainara","family":"Mira-Iglesias","sequence":"first","affiliation":[{"name":"Fundaci\u00f3n para el Fomento de la Investigaci\u00f3n Sanitaria y Biom\u00e9dica de la Comunitat Valenciana (FISABIO-Public Health), 46020-Val\u00e8ncia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9355-2909","authenticated-orcid":false,"given":"Esperanza","family":"Navarro-Pardo","sequence":"additional","affiliation":[{"name":"Department of Developmental and Educational Psychology, Universitat de Val\u00e8ncia, 46010-Val\u00e8ncia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3681-7533","authenticated-orcid":false,"given":"J. Alberto","family":"Conejero","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022-Val\u00e8ncia, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,18]]},"reference":[{"key":"ref_1","unstructured":"Gurd, J., Kischka, U., and Marshal, J. (2010). The Handbook of Clinical Neuropsychology, Oxford University Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1001\/jamapsychiatry.2013.277","article-title":"Meta-analysis of functional magnetic resonance imaging studies of inhibition and attention in attention-deficit\/hyperactivity disorder: Exploring task-specific, stimulant medication, and age effects","volume":"70","author":"Hart","year":"2013","journal-title":"JAMA Psychiatr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1080\/09602019108402257","article-title":"The use of a rating scale of attentional behavior","volume":"1","author":"Ponsford","year":"1991","journal-title":"Neuropsychol. Rehabil."},{"key":"ref_4","first-page":"175","article-title":"Conners\u2019 continuous performance Test II (CPT II v. 5)","volume":"29","author":"Conners","year":"2000","journal-title":"Multi-Health Syst. Inc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"116","DOI":"10.3758\/BF03195503","article-title":"DMDX: A Windows display program with millisecond accuracy","volume":"35","author":"Forster","year":"2003","journal-title":"Behav. Res. Methods Instrum. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"314","DOI":"10.3758\/s13428-011-0168-7","article-title":"OpenSesame: An open-source, graphical experiment builder for the social sciences","volume":"44","author":"Schreij","year":"2012","journal-title":"Behav. Res. Methods"},{"key":"ref_7","unstructured":"Spap\u00e9, M., Verdonschot, R., Dantzig, S.V., and Steenbergen, H.V. (2014). The E-Primer: An Introduction to Creating Psychological Experiments in E-Prime\u00ae, Leiden University Press."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Subcommittee on Attention-Deficit\/Hyperactivity Disorder, Steering committee on Quality Improvement and Management (2011). ADHD: Clinical practice guideline for the diagnosis, evaluation, and treatment of attention-deficit\/hyperactivity disorder in children and adolescents. Pediatrics, 128, 2011\u20132654.","DOI":"10.1542\/peds.2011-2654"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1034","DOI":"10.1542\/peds.2010-2989","article-title":"Trends in the prevalence of developmental disabilities in US children, 1997\u20132008","volume":"127","author":"Boyle","year":"2011","journal-title":"Pediatrics"},{"key":"ref_10","unstructured":"Barkley, R.A. (2014). Attention-Deficit Hyperactivity Disorder: A Handbook for Diagnosis and Treatment, Guilford Publications."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"e994","DOI":"10.1542\/peds.2014-3482","article-title":"Prevalence of attention-deficit\/hyperactivity disorder: A systematic review and meta-analysis","volume":"135","author":"Thomas","year":"2015","journal-title":"Pediatrics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1037\/a0027347","article-title":"Validity of DSM-IV attention deficit\/hyperactivity disorder symptom dimensions and subtypes","volume":"121","author":"Willcutt","year":"2012","journal-title":"J. Abnorm. Psychol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.jaac.2013.09.001","article-title":"Trends in the parent-report of health care provider-diagnosed and medicated attention-deficit\/hyperactivity disorder: United States, 2003\u20132011","volume":"53","author":"Visser","year":"2014","journal-title":"J. Am. Acad. Child Adolesc. Psychiatry"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.paid.2007.01.016","article-title":"Evidence for gender differences in visual selective attention","volume":"43","author":"Merritt","year":"2007","journal-title":"Pers. Individ. Differ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.visres.2009.10.010","article-title":"Differential development of visual attention skills in school-age children","volume":"50","author":"Dye","year":"2010","journal-title":"Vision Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1080\/00207450490422056","article-title":"Gender differences in event-related potentials during visual-spatial attention","volume":"114","author":"Vaquero","year":"2004","journal-title":"Int. J. Neurosci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1097\/00004583-198805000-00010","article-title":"Differential assessment of attention and impulsivity in children","volume":"27","author":"Halperin","year":"1988","journal-title":"J. Am. Acad. Child Adolesc. Psychiatry"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1177\/107319110100800401","article-title":"Sensitivity and specificity of a computerized test of Attention in the diagnosis of Attention-Deficit\/Hyperactivity Disorder","volume":"8","author":"Schatz","year":"2001","journal-title":"Assesment"},{"key":"ref_19","first-page":"357","article-title":"Gender differences in attention-deficit\/hyperactivity disorder","volume":"33","author":"Rucklidge","year":"2010","journal-title":"Psychiatr. Clin."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"15020","DOI":"10.1038\/nrdp.2015.20","article-title":"Attention-deficit\/hyperactivity disorder","volume":"1","author":"Faraone","year":"2015","journal-title":"Nat. Rev. Dis. Primers"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1176\/ajp.2007.164.6.942","article-title":"The worldwide prevalence of ADHD: A systematic review and metaregression analysis","volume":"164","author":"Polanczyk","year":"2007","journal-title":"Am. J. Psychiatry"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1036","DOI":"10.1097\/00004583-199708000-00011","article-title":"Gender differences in ADHD: A meta-analysis and critical review","volume":"36","author":"Gaub","year":"1997","journal-title":"J. Am. Acad. Child Adolesc. Psychiatry"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1177\/108705470200500302","article-title":"Meta-analysis gender differences ADHD","volume":"5","author":"Gershon","year":"2002","journal-title":"J. Atten. Disord."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1111\/jcpp.12337","article-title":"Sex differences in ADHD symptom severity","volume":"56","author":"Arnett","year":"2015","journal-title":"J. Child Psychol. Psychiatry"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1037\/0033-2909.125.3.367","article-title":"Gender differences in risk taking: A meta-analysis","volume":"125","author":"Byrnes","year":"1999","journal-title":"Psychol. Bull."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1162\/00335530360698496","article-title":"Performance in competitive environments: Gender differences","volume":"118","author":"Gneezy","year":"2003","journal-title":"Q. J. Econ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1162\/qjec.122.3.1067","article-title":"Do women shy away from competition? Do men compete too much?","volume":"122","author":"Niederle","year":"2007","journal-title":"Q. J. Econ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1037\/0022-0663.94.2.396","article-title":"Making the grade but feeling distressed: Gender differences in academic performance and internal distress","volume":"94","author":"Pomerantz","year":"2002","journal-title":"J. Educ. Psychol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1177\/0963721411408885","article-title":"Moving beyond the mean in studies of mental chronometry: The power of response time distributional analyses","volume":"20","author":"Balota","year":"2011","journal-title":"Curr. Dir. Psychol. Sci."},{"key":"ref_30","unstructured":"Luce, R.D. (1986). Response Times: Their Role in Inferring Elementary Mental Organization, Oxford University Press."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1037\/0033-295X.83.3.190","article-title":"Retrieval processes in recognition memory","volume":"83","author":"Ratcliff","year":"1976","journal-title":"Psychol. Rev."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"35","DOI":"10.20982\/tqmp.04.1.p035","article-title":"How to use MATLAB to fit the ex-Gaussian and other probability functions to a distribution of response times","volume":"4","author":"Lacouture","year":"2008","journal-title":"Tutor. Quant. Methods Psychol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1023\/A:1025457300409","article-title":"Continuous performance test performance in a normative epidemiological sample","volume":"31","author":"Conners","year":"2003","journal-title":"J. Abnorm. Child Psychol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1080\/09297040802646991","article-title":"Intra-individual variability among children with ADHD on a working memory task: An ex-Gaussian approach","volume":"15","author":"Buzy","year":"2009","journal-title":"Child Neuropsychol."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Gmehlin, D., Fuermaier, A.B., Walther, S., Debelak, R., Rentrop, M., Westermann, C., Sharma, A., Tucha, L., Koerts, J., and Tucha, O. (2014). Intraindividual variability in inhibitory function in adults with ADHD\u2014An ex-Gaussian approach. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0112298"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3709","DOI":"10.1016\/j.ridd.2013.07.025","article-title":"The ex-Gaussian distribution of reaction times in adolescents with attention-deficit\/hyperactivity disorder","volume":"34","author":"Gu","year":"2013","journal-title":"Res. Dev. Disabil."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"370","DOI":"10.5334\/pb.240","article-title":"The effect of corrective feedback on performance in basic cognitive tasks: An analysis of RT components","volume":"56","author":"Irigaray","year":"2016","journal-title":"Psychol. Belg."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1111\/sjop.12136","article-title":"The effects of age and emotional valence on recognition memory: An ex-Gaussian components analysis","volume":"55","author":"Argimon","year":"2014","journal-title":"Scand. J. Psychol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Albert","year":"1999","journal-title":"Science"},{"key":"ref_40","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_41","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1137\/070710111","article-title":"Power-law Distributions in Empirical Data","volume":"51","author":"Clauset","year":"2009","journal-title":"SIAM Rev."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.endm.2016.09.058","article-title":"Natural visibility graphs for diagnosing attention deficit hyperactivity disorder (ADHD)","volume":"54","author":"Conejero","year":"2016","journal-title":"Electron. Notes Discrete Math."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"14931","DOI":"10.1073\/pnas.0506897102","article-title":"Training, maturation, and genetic influences on the development of executive attention","volume":"102","author":"Rueda","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4972","DOI":"10.1073\/pnas.0709247105","article-title":"From time series to complex networks: The visibility graph","volume":"105","author":"Lacasa","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"335002","DOI":"10.1088\/1751-8113\/43\/33\/335002","article-title":"Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices","volume":"43","author":"Qian","year":"2010","journal-title":"J. Phys. A"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physa.2016.06.051","article-title":"Visibility graph network analysis of natural gas price: The case of North American market","volume":"462","author":"Sun","year":"2016","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"7798","DOI":"10.3390\/e17117798","article-title":"Word-length correlations and memory in large texts: A visibility network analysis","volume":"17","author":"Liebovitch","year":"2015","journal-title":"Entropy"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"L16702","DOI":"10.1029\/2009GL039129","article-title":"Visibility network of United States hurricanes","volume":"36","author":"Elsner","year":"2009","journal-title":"Geophys. Res. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1140\/epjb\/e2013-40762-2","article-title":"Earthquake magnitude time series: Scaling behavior of visibility networks","volume":"86","year":"2013","journal-title":"Eur. Phys. J. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"50002","DOI":"10.1209\/0295-5075\/97\/50002","article-title":"Analysis of seismic sequences by using the method of visibility graph","volume":"97","author":"Telesca","year":"2012","journal-title":"EPL Europhys. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1007\/s00702-010-0450-3","article-title":"New diagnostic EEG markers of the Alzheimer\u2019s disease using visibility graph","volume":"117","author":"Ahmadlou","year":"2010","journal-title":"J. Neural Transm."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"4720","DOI":"10.1016\/j.physa.2012.04.025","article-title":"Improved visibility graph fractality with application for the diagnosis of autism spectrum disorder","volume":"391","author":"Ahmadlou","year":"2012","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.physd.2013.06.009","article-title":"Evolving networks in the human epileptic brain","volume":"267","author":"Lehnertz","year":"2014","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1813","DOI":"10.1109\/JBHI.2014.2303991","article-title":"Analysis and classification of sleep stages based on difference visibility graphs from a single-channel EEG signal","volume":"18","author":"Zhu","year":"2014","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_55","unstructured":"Barab\u00e1si, A.L. (2016). Network Science, Cambridge University Press."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"30001","DOI":"10.1209\/0295-5075\/86\/30001","article-title":"The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion","volume":"86","author":"Lacasa","year":"2009","journal-title":"EPL Europhys. Lett."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1137\/S003614450342480","article-title":"The structure and function of complex networks","volume":"45","author":"Newman","year":"2003","journal-title":"SIAM Rev."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1080\/00018730110112519","article-title":"Evolution of networks","volume":"51","author":"Dorogovtsev","year":"2002","journal-title":"Adv. Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1038\/nature03248","article-title":"Self-similarity of complex networks","volume":"433","author":"Song","year":"2005","journal-title":"Nature"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"45","DOI":"10.21042\/AMNS.2016.1.00004","article-title":"Complex network theory and its application research on P2P networks","volume":"1","author":"Jian","year":"2016","journal-title":"Appl. Math. Nonlinear Sci."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/j.cpr.2013.06.001","article-title":"Reaction time variability in ADHD: A meta-analytic review of 319 studies","volume":"33","author":"Kofler","year":"2013","journal-title":"Clin. Psychol. Rev."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1111\/sjop.12372","article-title":"Age slowing down in detection and visual discrimination under varying presentation times","volume":"58","author":"Gamermann","year":"2017","journal-title":"Scand. J. Psychol."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1037\/a0039658","article-title":"Sequential processes and the shapes of reaction time distributions","volume":"122","author":"Sternberg","year":"2015","journal-title":"Psychol. Rev."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"2389","DOI":"10.1016\/j.neuropsychologia.2009.01.022","article-title":"Increased intra-individual reaction time y in attention-deficit\/hyperactivity disorder across response inhibition tasks with different cognitive demands","volume":"47","author":"Vaurio","year":"2009","journal-title":"Neuropsychologia"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Luque, B., Lacasa, L., Ballesteros, F.J., and Robledo, A. (2011). Feigenbaum graphs: A complex network perspective of chaos. PLoS ONE, 6.","DOI":"10.1371\/journal.pone.0022411"},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Iglesias Mart\u00ednez, M.E., Garc\u00eda-Gomez, J.M., S\u00e1ez, C., Fern\u00e1ndez de C\u00f3rdoba, P., and Conejero, J.A. (2018). Feature extraction and similarity of movement detection during sleep, based on higher order spectra and entropy of the actigraphy signal: Results of the Hispanic Community Health Study\/Study of Latinos. Sensors, 18.","DOI":"10.3390\/s18124310"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"239","DOI":"10.21042\/AMNS.2016.1.00018","article-title":"Vibrational resonance: A study with high-order word-series averaging","volume":"1","author":"Murua","year":"2016","journal-title":"Appl. Math. Nonlinear Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/563\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:46:32Z","timestamp":1760186792000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/563"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,18]]},"references-count":67,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["sym11040563"],"URL":"https:\/\/doi.org\/10.3390\/sym11040563","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,4,18]]}}}