{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T09:15:00Z","timestamp":1765444500932,"version":"3.46.0"},"reference-count":80,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T00:00:00Z","timestamp":1760832000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T00:00:00Z","timestamp":1760832000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100017642","name":"Spanish National Plan for Scientific and Technical Research and Innovation","doi-asserted-by":"publisher","award":["PI15\/00587","PI18\/01030","PI21\/01189"],"award-info":[{"award-number":["PI15\/00587","PI18\/01030","PI21\/01189"]}],"id":[{"id":"10.13039\/501100017642","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PID2021-128966NB-I00"],"award-info":[{"award-number":["PID2021-128966NB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PID2024-157778OB-I00"],"award-info":[{"award-number":["PID2024-157778OB-I00"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011104","name":"Universitat Aut\u00f2noma de Barcelona","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100011104","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Health Inf Sci Syst"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Brain networks, or graphs, derived from magnetic resonance imaging (MRI) offer a powerful framework for representing the structural, morphological, and functional organization of the brain. Graph-theoretical metrics have been widely employed to characterize properties such as efficiency, integration, and communication within these networks. More recently, topological data analysis techniques, such as persistent homology and Betti curves, have emerged as complementary approaches for capturing higher-order network patterns. In this study, we present a comparative analysis of these feature-generation methodologies in the context of neurodegenerative disease. Specifically, we evaluate the effectiveness of Betti curves and graph-theoretical metrics in extracting features for distinguishing people with multiple sclerosis (PwMS) from healthy volunteers (HV). Features are derived from structural connectivity, morphological gray matter, and resting-state functional networks, using both single layer and multilayer graph architectures. Our experiments, conducted on a cohort of PwMS and HV, demonstrate that features extracted using Betti curves generally outperform those based on graph-theoretical metrics. Furthermore, we show that multimodal data in terms of feature concatenation and multilayer graph architectures provide a more comprehensive representation of alterations in complex brain mechanisms associated with MS, leading to improved classification performance. These findings highlight the potential of topological features and multimodal integration for enhancing the understanding and diagnosis of neurodegenerative disorders.<\/jats:p>","DOI":"10.1007\/s13755-025-00386-y","type":"journal-article","created":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T13:23:03Z","timestamp":1760880183000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Evaluating topological and graph-theoretical approaches to extract complex multimodal brain connectivity patterns in multiple sclerosis"],"prefix":"10.1007","volume":"13","author":[{"given":"Toni","family":"Lozano-Bag\u00e9n","sequence":"first","affiliation":[]},{"given":"Eloy","family":"Martinez-Heras","sequence":"additional","affiliation":[]},{"given":"Giuseppe","family":"Pontillo","sequence":"additional","affiliation":[]},{"given":"Elisabeth","family":"Solana","sequence":"additional","affiliation":[]},{"given":"Francesc","family":"Viv\u00f3","sequence":"additional","affiliation":[]},{"given":"Maria","family":"Petracca","sequence":"additional","affiliation":[]},{"given":"Alberto","family":"Calvi","sequence":"additional","affiliation":[]},{"given":"Sandra","family":"Garrido-Romero","sequence":"additional","affiliation":[]},{"given":"Albert","family":"Sol\u00e9-Ribalta","sequence":"additional","affiliation":[]},{"given":"Sara","family":"Llufriu","sequence":"additional","affiliation":[]},{"given":"Ferran","family":"Prados","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0617-3303","authenticated-orcid":false,"given":"Jordi","family":"Casas-Roma","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,19]]},"reference":[{"issue":"7","key":"386_CR1","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1016\/j.neubiorev.2013.04.008","volume":"37","author":"IJ Bennett","year":"2013","unstructured":"Bennett IJ, Rypma B. Advances in functional neuroanatomy: A review of combined dti and fmri studies in healthy younger and older adults. Neurosci Biobehav Rev. 2013;37(7):1201\u201310. https:\/\/doi.org\/10.1016\/j.neubiorev.2013.04.008.","journal-title":"Neurosci Biobehav Rev"},{"issue":"4","key":"386_CR2","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1093\/braincomms\/fcab237","volume":"3","author":"S Groppa","year":"2021","unstructured":"Groppa S, Gonzalez-Escamilla G, Eshaghi A, Meuth SG, Ciccarelli O. Linking immune-mediated damage to neurodegeneration in multiple sclerosis: could network-based mri help? Brain Commun. 2021;3(4):237. https:\/\/doi.org\/10.1093\/braincomms\/fcab237.","journal-title":"Brain Commun"},{"key":"386_CR3","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1016\/j.nicl.2016.11.026","volume":"13","author":"S Llufriu","year":"2017","unstructured":"Llufriu S, Martinez-Heras E, Solana E, Sola-Valls N, Sepulveda M, Blanco Y, et al. Structural networks involved in attention and executive functions in multiple sclerosis. NeuroImage: Clinical. 2017;13:288\u201396. https:\/\/doi.org\/10.1016\/j.nicl.2016.11.026.","journal-title":"NeuroImage: Clinical"},{"issue":"7","key":"386_CR4","doi-asserted-by":"publisher","first-page":"1530","DOI":"10.1093\/cercor\/bhr221","volume":"22","author":"BM Tijms","year":"2012","unstructured":"Tijms BM, Seri\u00e9s P, Willshaw DJ, Lawrie SM. Similarity-based extraction of individual networks from gray matter mri scans. Cereb Cortex. 2012;22(7):1530\u201341. https:\/\/doi.org\/10.1093\/cercor\/bhr221.","journal-title":"Cereb Cortex"},{"issue":"15","key":"386_CR5","doi-asserted-by":"publisher","first-page":"2672","DOI":"10.1212\/WNL.96.15_supplement.2672","volume":"96","author":"MA Rocca","year":"2021","unstructured":"Rocca MA, Valsasina P, Marchesi O, Preziosa P, Sona D, Tessadori J, et al. The role of brain network functional connectivity and machine learning for the classification and characterization of disease phenotypes in patients with multiple sclerosis. Neurology. 2021;96(15):2672. https:\/\/doi.org\/10.1212\/WNL.96.15_supplement.2672.","journal-title":"Neurology"},{"issue":"4","key":"386_CR6","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1109\/TBDATA.2017.2734883","volume":"3","author":"A Phinyomark","year":"2017","unstructured":"Phinyomark A, Ib\u00e1\u00f1ez-Marcelo E, Petri G. Resting-state fmri functional connectivity: big data preprocessing pipelines and topological data analysis. IEEE Trans on Big Data. 2017;3(4):415\u201328. https:\/\/doi.org\/10.1109\/TBDATA.2017.2734883.","journal-title":"IEEE Trans on Big Data"},{"issue":"3","key":"386_CR7","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1038\/nrn2575","volume":"10","author":"E Bullmore","year":"2009","unstructured":"Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci. 2009;10(3):186\u201398.","journal-title":"Nat Rev Neurosci"},{"issue":"2","key":"386_CR8","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.conb.2012.11.015","volume":"23","author":"O Sporns","year":"2013","unstructured":"Sporns O. Network attributes for segregation and integration in the human brain. Curr Opin Neurobiol. 2013;23(2):162\u201371. https:\/\/doi.org\/10.1016\/j.conb.2012.11.015.","journal-title":"Curr Opin Neurobiol"},{"key":"386_CR9","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.plrev.2023.12.006","volume":"48","author":"D Papo","year":"2024","unstructured":"Papo D, Buld\u00fa JM. Does the brain behave like a (complex) network? i. dynamics. Phys Life Rev. 2024;48:47\u201398.","journal-title":"Phys Life Rev"},{"issue":"3","key":"386_CR10","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1016\/j.plrev.2014.03.005","volume":"11","author":"L Pessoa","year":"2014","unstructured":"Pessoa L. Understanding brain networks and brain organization. Phys Life Rev. 2014;11(3):400\u201335.","journal-title":"Phys Life Rev"},{"issue":"3","key":"386_CR11","doi-asserted-by":"publisher","first-page":"247","DOI":"10.31887\/DCNS.2013.15.3\/osporns","volume":"15","author":"O Sporns","year":"2013","unstructured":"Sporns O. Structure and function of complex brain networks. Dialogues Clin Neurosci. 2013;15(3):247\u201362.","journal-title":"Dialogues Clin Neurosci"},{"issue":"2","key":"386_CR12","doi-asserted-by":"publisher","first-page":"111","DOI":"10.31887\/DCNS.2018.20.2\/osporns","volume":"20","author":"O Sporns","year":"2018","unstructured":"Sporns O. Graph theory methods: applications in brain networks. Dialogues Clin Neurosci. 2018;20(2):111\u201321.","journal-title":"Dialogues Clin Neurosci"},{"issue":"6","key":"386_CR13","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1177\/1073858406293182","volume":"12","author":"DS Bassett","year":"2006","unstructured":"Bassett DS, Bullmore ED. Small-world brain networks. The Neuroscientist. 2006;12(6):512\u201323.","journal-title":"The Neuroscientist"},{"issue":"5","key":"386_CR14","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1038\/s42254-019-0040-8","volume":"1","author":"CW Lynn","year":"2019","unstructured":"Lynn CW, Bassett DS. The physics of brain network structure, function and control. Nat Rev Phys. 2019;1(5):318\u201332.","journal-title":"Nat Rev Phys"},{"issue":"4","key":"386_CR15","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1089\/brain.2011.0055","volume":"1","author":"QK Telesford","year":"2011","unstructured":"Telesford QK, Simpson SL, Burdette JH, Hayasaka S, Laurienti PJ. The brain as a complex system: using network science as a tool for understanding the brain. Brain Connectivity. 2011;1(4):295\u2013308.","journal-title":"Brain Connectivity"},{"issue":"2","key":"386_CR16","first-page":"56","volume":"22","author":"M-T Kuhnert","year":"2012","unstructured":"Kuhnert M-T, Geier C, Elger CE, Lehnertz K. Identifying important nodes in weighted functional brain networks: a comparison of different centrality approaches. Chaos. Interdisc J Nonlinear Sci. 2012;22(2):56\u201389.","journal-title":"Interdisc J Nonlinear Sci"},{"issue":"6","key":"386_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.98.062413","volume":"98","author":"VV Makarov","year":"2018","unstructured":"Makarov VV, Zhuravlev MO, Runnova AE, Protasov P, Maksimenko VA, Frolov NS, et al. Betweenness centrality in multiplex brain network during mental task evaluation. Phys Rev E. 2018;98(6):062413.","journal-title":"Phys Rev E"},{"issue":"1","key":"386_CR18","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1146\/annurev-psych-122414-033634","volume":"67","author":"O Sporns","year":"2016","unstructured":"Sporns O, Betzel RF. Modular brain networks. Annu Rev Psychol. 2016;67(1):613\u201340.","journal-title":"Annu Rev Psychol"},{"issue":"1","key":"386_CR19","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1146\/annurev.resource.102308.124234","volume":"1","author":"K Gillingham","year":"2009","unstructured":"Gillingham K, Newell RG, Palmer K. Energy efficiency economics and policy. Annu Rev Resour Econ. 2009;1(1):597\u2013620.","journal-title":"Annu Rev Resour Econ"},{"key":"386_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jneumeth.2020.108799","volume":"343","author":"I Bilgen","year":"2020","unstructured":"Bilgen I, Guvercin G, Rekik I. Machine learning methods for brain network classification: application to autism diagnosis using cortical morphological networks. J Neurosci Methods. 2020;343:108799.","journal-title":"J Neurosci Methods"},{"issue":"1","key":"386_CR21","doi-asserted-by":"publisher","first-page":"8072","DOI":"10.1038\/s41598-023-34650-6","volume":"13","author":"CL Alves","year":"2023","unstructured":"Alves CL, Toutain TG, Carvalho Aguiar P, Pineda AM, Roster K, Thielemann C, et al. Diagnosis of autism spectrum disorder based on functional brain networks and machine learning. Sci Rep. 2023;13(1):8072.","journal-title":"Sci Rep"},{"key":"386_CR22","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.cobeha.2017.09.005","volume":"19","author":"L Pessoa","year":"2018","unstructured":"Pessoa L. Understanding emotion with brain networks. Curr Opin Behav Sci. 2018;19:19\u201325.","journal-title":"Curr Opin Behav Sci"},{"issue":"6","key":"386_CR23","doi-asserted-by":"publisher","first-page":"735","DOI":"10.3390\/brainsci11060735","volume":"11","author":"I Ivanoska","year":"2021","unstructured":"Ivanoska I, Trivodaliev K, Kalajdziski S, Zanin M. Statistical and machine learning link selection methods for brain functional networks: Review and comparison. Brain Sci. 2021;11(6):735.","journal-title":"Brain Sci"},{"issue":"1","key":"386_CR24","doi-asserted-by":"publisher","first-page":"5573740","DOI":"10.1155\/2021\/5573740","volume":"2021","author":"S Wein","year":"2021","unstructured":"Wein S, Deco G, Tom\u00e9 AM, Goldhacker M, Malloni WM, Greenlee MW, et al. Brain connectivity studies on structure-function relationships: A short survey with an emphasis on machine learning. Comput Intell Neurosci. 2021;2021(1):5573740.","journal-title":"Comput Intell Neurosci"},{"issue":"5","key":"386_CR25","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1001\/jamapsychiatry.2019.3671","volume":"77","author":"RA Poldrack","year":"2020","unstructured":"Poldrack RA, Huckins G, Varoquaux G. Establishment of best practices for evidence for prediction: A review. JAMA Psychiat. 2020;77(5):534\u201340. https:\/\/doi.org\/10.1001\/jamapsychiatry.2019.3671.","journal-title":"JAMA Psychiat"},{"issue":"4","key":"386_CR26","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1089\/brain.2014.0313","volume":"5","author":"T Welton","year":"2015","unstructured":"Welton T, Kent DA, Auer DP, Dineen RA. Reproducibility of graph-theoretic brain network metrics: a systematic review. Brain Connectivity. 2015;5(4):193\u2013202.","journal-title":"Brain Connectivity"},{"issue":"3","key":"386_CR27","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.1016\/j.neuroimage.2009.10.003","volume":"52","author":"M Rubinov","year":"2010","unstructured":"Rubinov M, Sporns O. Complex network measures of brain connectivity: uses and interpretations. Neuroimage. 2010;52(3):1059\u201369.","journal-title":"Neuroimage"},{"issue":"2","key":"386_CR28","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1177\/1352458518820759","volume":"26","author":"E Pagani","year":"2020","unstructured":"Pagani E, Rocca MA, Meo ED, Horsfield MA, Colombo B, Rodegher M, et al. Structural connectivity in multiple sclerosis and modeling of disconnection. Mult Scler J. 2020;26(2):220\u201332. https:\/\/doi.org\/10.1177\/1352458518820759.","journal-title":"Mult Scler J"},{"issue":"1","key":"386_CR29","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/s00429-014-0896-4","volume":"221","author":"MA Rocca","year":"2016","unstructured":"Rocca MA, Valsasina P, Meani A, Falini A, Comi G, Filippi M. Impaired functional integration in multiple sclerosis: a graph theory study. Brain Struct Funct. 2016;221(1):115\u201331. https:\/\/doi.org\/10.1007\/s00429-014-0896-4.","journal-title":"Brain Struct Funct"},{"key":"386_CR30","first-page":"21","volume":"6","author":"MD Sacchet","year":"2015","unstructured":"Sacchet MD, Prasad G, Foland-Ross LC, Thompson PM, Gotlib IH. Support vector machine classification of major depressive disorder using diffusion-weighted neuroimaging and graph theory. Front Psych. 2015;6:21.","journal-title":"Front Psych"},{"key":"386_CR31","doi-asserted-by":"crossref","unstructured":"Wang W, Xu X, Yao X, Zhou L, Wu T. Machine learning of brain functional network characteristics for ad classification. In: International Conference on Image, Vision and Intelligent Systems, 2023;590\u2013599. Springer.","DOI":"10.1007\/978-981-97-0855-0_57"},{"key":"386_CR32","doi-asserted-by":"publisher","first-page":"111832","DOI":"10.1109\/ACCESS.2023.3323250","volume":"11","author":"L Wang","year":"2023","unstructured":"Wang L, Sheng J, Zhang Q, Zhou R, Li Z, Xin Y, et al. Functional brain network measures for alzheimer\u2019s disease classification. IEEE Access. 2023;11:111832\u201345.","journal-title":"IEEE Access"},{"key":"386_CR33","doi-asserted-by":"publisher","first-page":"479","DOI":"10.3389\/fbioe.2019.00479","volume":"7","author":"Y Xiang","year":"2020","unstructured":"Xiang Y, Wang J, Tan G, Wu F-X, Liu J. Schizophrenia identification using multi-view graph measures of functional brain networks. Front Bioeng Biotechnol. 2020;7:479.","journal-title":"Front Bioeng Biotechnol"},{"issue":"2","key":"386_CR34","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1017\/S1355617715000867","volume":"22","author":"RA Yeo","year":"2016","unstructured":"Yeo RA, Ryman SG, Van Den Heuvel MP, De Reus MA, Jung RE, Pommy J, et al. Graph metrics of structural brain networks in individuals with schizophrenia and healthy controls: group differences, relationships with intelligence, and genetics. J Int Neuropsychol Soc. 2016;22(2):240\u20139.","journal-title":"J Int Neuropsychol Soc"},{"issue":"11","key":"386_CR35","doi-asserted-by":"publisher","first-page":"1852","DOI":"10.1017\/S0033291719001934","volume":"50","author":"D Lei","year":"2020","unstructured":"Lei D, Pinaya WH, Van Amelsvoort T, Marcelis M, Donohoe G, Mothersill DO, et al. Detecting schizophrenia at the level of the individual: relative diagnostic value of whole-brain images, connectome-wide functional connectivity and graph-based metrics. Psychol Med. 2020;50(11):1852\u201361.","journal-title":"Psychol Med"},{"key":"386_CR36","doi-asserted-by":"publisher","first-page":"28","DOI":"10.3389\/fnagi.2020.00028","volume":"12","author":"X Xu","year":"2020","unstructured":"Xu X, Li W, Mei J, Tao M, Wang X, Zhao Q, et al. Feature selection and combination of information in the functional brain connectome for discrimination of mild cognitive impairment and analyses of altered brain patterns. Front Aging Neurosci. 2020;12:28.","journal-title":"Front Aging Neurosci"},{"issue":"10","key":"386_CR37","doi-asserted-by":"publisher","first-page":"3015","DOI":"10.19026\/rjaset.5.4616","volume":"5","author":"H Guo","year":"2013","unstructured":"Guo H, Cao X, Liu Z, Chen J. Abnormal functional brain network metrics for machine learning classifier in depression patients identification. Res J Appl Sci Eng Technol. 2013;5(10):3015\u201320.","journal-title":"Res J Appl Sci Eng Technol"},{"key":"386_CR38","doi-asserted-by":"publisher","DOI":"10.1016\/j.pnpbp.2021.110401","volume":"111","author":"J-Y Yun","year":"2021","unstructured":"Yun J-Y, Kim Y-K. Graph theory approach for the structural-functional brain connectome of depression. Prog Neuropsychopharmacol Biol Psychiatry. 2021;111:110401.","journal-title":"Prog Neuropsychopharmacol Biol Psychiatry"},{"issue":"3","key":"386_CR39","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1162\/netn_a_00258","volume":"6","author":"J Casas-Roma","year":"2022","unstructured":"Casas-Roma J, Martinez-Heras E, Sol\u00e9-Ribalta A, Solana E, Lopez-Soley E, Viv\u00f3 F, et al. Applying multilayer analysis to morphological, structural, and functional brain networks to identify relevant dysfunction patterns. Netw Neurosci. 2022;6(3):916\u201333. https:\/\/doi.org\/10.1162\/netn_a_00258.","journal-title":"Netw Neurosci"},{"key":"386_CR40","doi-asserted-by":"publisher","DOI":"10.3389\/frai.2021.667963","volume":"4","author":"F Chazal","year":"2021","unstructured":"Chazal F, Michel B. An introduction to topological data analysis: fundamental and practical aspects for data scientists. Front Artif Intel. 2021;4:667963.","journal-title":"Front Artif Intel"},{"key":"386_CR41","doi-asserted-by":"publisher","DOI":"10.1109\/isbi.2011.5872535","author":"H Lee","year":"2011","unstructured":"Lee H, Chung MK, Kang H, Kim B-N, Lee DS. Discriminative persistent homology of brain networks. IEEE International Symposium on Biomedical Imaging: From Nano to Macro. 2011. https:\/\/doi.org\/10.1109\/isbi.2011.5872535.","journal-title":"IEEE International Symposium on Biomedical Imaging: From Nano to Macro"},{"key":"386_CR42","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1527\/tjsai.D-G72","volume":"227","author":"EGZ Centeno","year":"2022","unstructured":"Centeno EGZ, Moreni G, Vriend C, Douw L, Santos FAN. A hands-on tutorial on network and topological neuroscience. Brain Struct Function. 2022;227:741\u201362. https:\/\/doi.org\/10.1527\/tjsai.D-G72.","journal-title":"Brain Struct Function"},{"key":"386_CR43","doi-asserted-by":"publisher","DOI":"10.3389\/fnagi.2022.788571","author":"J Xing","year":"2022","unstructured":"Xing J, Jia J, Wu X, Kuang L. A spatiotemporal brain network analysis of Alzheimer\u2019s disease based on persistent homology. Front Aging Neurosci. 2022. https:\/\/doi.org\/10.3389\/fnagi.2022.788571.","journal-title":"Front Aging Neurosci"},{"key":"386_CR44","doi-asserted-by":"publisher","DOI":"10.3389\/fphys.2023.1227952","author":"Z Wang","year":"2023","unstructured":"Wang Z, Liu F, Shi S, Xia S, Peng F, Wang L, et al. Automatic epileptic seizure detection based on persistent homology. Front Physiol. 2023. https:\/\/doi.org\/10.3389\/fphys.2023.1227952.","journal-title":"Front Physiol"},{"key":"386_CR45","doi-asserted-by":"publisher","DOI":"10.3389\/fncom.2022.1024205","author":"G Guo","year":"2022","unstructured":"Guo G, Zhao Y, Liu C, Fu Y, Xi X, Jin L, et al. Method for persistent topological features extraction of schizophrenia patients\u2019 electroencephalography signal based on persistent homology. Front Comput Neurosci. 2022. https:\/\/doi.org\/10.3389\/fncom.2022.1024205.","journal-title":"Front Comput Neurosci"},{"key":"386_CR46","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2021.118245","volume":"238","author":"L Caputi","year":"2021","unstructured":"Caputi L, Pidnebesna A, Hlinka J. Promises and pitfalls of topological data analysis for brain connectivity analysis. NeuroImage. 2021;238:118245. https:\/\/doi.org\/10.1016\/j.neuroimage.2021.118245.","journal-title":"NeuroImage"},{"issue":"12","key":"386_CR47","doi-asserted-by":"publisher","first-page":"1055","DOI":"10.30773\/pi.2022.0174","volume":"19","author":"N Yoon","year":"2022","unstructured":"Yoon N, Huh Y, Lee H, Kim JI, Lee J, Yang C-M, et al. Alterations in social brain network topology at rest in children with autism spectrum disorder. Psychiatry Investigation. 2022;19(12):1055\u201368. https:\/\/doi.org\/10.30773\/pi.2022.0174.","journal-title":"Psychiatry Investigation"},{"key":"386_CR48","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/j.neuroimage.2019.06.044","volume":"200","author":"E Ib\u00e1\u00f1ez-Marcelo","year":"2019","unstructured":"Ib\u00e1\u00f1ez-Marcelo E, Campioni L, Phinyomark A, Petri G, Santarcangelo EL. Topology highlights mesoscopic functional equivalence between imagery and perception: The case of hypnotizability. NeuroImage. 2019;200:437\u201349. https:\/\/doi.org\/10.1016\/j.neuroimage.2019.06.044.","journal-title":"NeuroImage"},{"issue":"7","key":"386_CR49","doi-asserted-by":"publisher","first-page":"5169","DOI":"10.1007\/s10462-022-10146-z","volume":"55","author":"CS Pun","year":"2022","unstructured":"Pun CS, Lee SX, Xia K. Persistent-homology-based machine learning: a survey and a comparative study. Artif Intell Rev. 2022;55(7):5169\u2013213. https:\/\/doi.org\/10.1007\/s10462-022-10146-z.","journal-title":"Artif Intell Rev"},{"key":"386_CR50","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2021.102233","volume":"74","author":"X Li","year":"2021","unstructured":"Li X, Zhou Y, Dvornek N, Zhang M, Gao S, Zhuang J, et al. Braingnn: interpretable brain graph neural network for fmri analysis. Med Image Anal. 2021;74:102233.","journal-title":"Med Image Anal"},{"key":"386_CR51","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2023.107913","volume":"243","author":"C Dong","year":"2024","unstructured":"Dong C, Sun D. Brain network classification based on dynamic graph attention information bottleneck. Comput Methods Programs Biomed. 2024;243:107913.","journal-title":"Comput Methods Programs Biomed"},{"key":"386_CR52","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2020.104096","volume":"127","author":"H Jiang","year":"2020","unstructured":"Jiang H, Cao P, Xu M, Yang J, Zaiane O. Hi-gcn: a hierarchical graph convolution network for graph embedding learning of brain network and brain disorders prediction. Comput Biol Med. 2020;127:104096.","journal-title":"Comput Biol Med"},{"key":"386_CR53","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2025.107450","volume":"188","author":"Y Luo","year":"2025","unstructured":"Luo Y, Chen Q, Li F, Yi L, Xu P, Zhang Y. Hierarchical feature extraction on functional brain networks for autism spectrum disorder identification with resting-state fmri data. Neural Netw. 2025;188:107450.","journal-title":"Neural Netw"},{"key":"386_CR54","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.neuroscience.2017.10.033","volume":"403","author":"V Fleischer","year":"2019","unstructured":"Fleischer V, Radetz A, Ciolac D, Muthuraman M, Gonzalez-Escamilla G, Zipp F, et al. Graph theoretical framework of brain networks in multiple sclerosis: a review of concepts. Neuroscience. 2019;403:35\u201353.","journal-title":"Neuroscience"},{"issue":"11","key":"386_CR55","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1136\/jnnp-2023-331531","volume":"94","author":"E Martinez-Heras","year":"2023","unstructured":"Martinez-Heras E, Solana E, Viv\u00f3 F, Lopez-Soley E, Calvi A, Alba-Arbalat S, et al. Diffusion-based structural connectivity patterns of multiple sclerosis phenotypes. J Neurol Neurosurg Psychiatr. 2023;94(11):916\u201323. https:\/\/doi.org\/10.1136\/jnnp-2023-331531.","journal-title":"J Neurol Neurosurg Psychiatr"},{"issue":"3","key":"386_CR56","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1038\/s41582-020-00439-8","volume":"17","author":"DT Chard","year":"2021","unstructured":"Chard DT, Alahmadi AAS, Audoin B, Charalambous T, Enzinger C, Hulst HE, et al. Mind the gap: from neurons to networks to outcomes in multiple sclerosis. Nat Rev Neurol. 2021;17(3):173\u201384. https:\/\/doi.org\/10.1038\/s41582-020-00439-8.","journal-title":"Nat Rev Neurol"},{"issue":"2","key":"386_CR57","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/S1474-4422(17)30470-2","volume":"17","author":"AJ Thompson","year":"2018","unstructured":"Thompson AJ, Banwell BL, Barkhof F, Carroll WM, Coetzee T, Comi G, et al. Diagnosis of multiple sclerosis: 2017 revisions of the mcdonald criteria. Lancet Neurol. 2018;17(2):162\u201373. https:\/\/doi.org\/10.1016\/S1474-4422(17)30470-2.","journal-title":"Lancet Neurol"},{"issue":"9","key":"386_CR58","doi-asserted-by":"publisher","first-page":"2062","DOI":"10.1002\/hbm.21344","volume":"33","author":"M Battaglini","year":"2011","unstructured":"Battaglini M, Jenkinson M, De Stefano N. Evaluating and reducing the impact of white matter lesions on brain volume measurements. Hum Brain Mapp. 2011;33(9):2062\u201371. https:\/\/doi.org\/10.1002\/hbm.21344.","journal-title":"Hum Brain Mapp"},{"issue":"3","key":"386_CR59","doi-asserted-by":"publisher","first-page":"968","DOI":"10.1016\/j.neuroimage.2006.01.021","volume":"31","author":"RS Desikan","year":"2006","unstructured":"Desikan RS, S\u00e9gonne F, Fischl B, Quinn BT, Dickerson BC, Blacker D, et al. An automated labeling system for subdividing the human cerebral cortex on mri scans into gyral based regions of interest. Neuroimage. 2006;31(3):968\u201380. https:\/\/doi.org\/10.1016\/j.neuroimage.2006.01.021.","journal-title":"Neuroimage"},{"key":"386_CR60","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2019.116137","volume":"202","author":"J-D Tournier","year":"2019","unstructured":"Tournier J-D, Smith R, Raffelt D, Tabbara R, Dhollander T, Pietsch M, et al. Mrtrix3: A fast, flexible and open software framework for medical image processing and visualisation. NeuroImage. 2019;202:116137. https:\/\/doi.org\/10.1016\/j.neuroimage.2019.116137.","journal-title":"NeuroImage"},{"key":"386_CR61","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1016\/j.neuroimage.2014.07.061","volume":"103","author":"B Jeurissen","year":"2014","unstructured":"Jeurissen B, Tournier J-D, Dhollander T, Connelly A, Sijbers J. Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion mri data. NeuroImage. 2014;103:411\u201326. https:\/\/doi.org\/10.1016\/j.neuroimage.2014.07.061.","journal-title":"NeuroImage"},{"issue":"5","key":"386_CR62","doi-asserted-by":"publisher","first-page":"833","DOI":"10.3174\/ajnr.A2894","volume":"33","author":"YH Chou","year":"2012","unstructured":"Chou YH, Panych LP, Dickey CC, Petrella JR, Chen NK. Investigation of long-term reproducibility of intrinsic connectivity network mapping: a resting-state fMRI study. Am J Neuroradiol. 2012;33(5):833\u20138. https:\/\/doi.org\/10.3174\/ajnr.A2894.","journal-title":"Am J Neuroradiol"},{"issue":"5","key":"386_CR63","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1053\/j.sult.2021.07.006","volume":"42","author":"E Martinez-Heras","year":"2021","unstructured":"Martinez-Heras E, Grussu F, Prados F, Solana E, Llufriu S. Diffusion-weighted imaging: recent advances and applications. Seminars Ultrasound CT and MRI. 2021;42(5):490\u2013506. https:\/\/doi.org\/10.1053\/j.sult.2021.07.006.","journal-title":"Seminars Ultrasound CT and MRI"},{"key":"386_CR64","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1038\/s42254-020-00249-3","volume":"2","author":"G Carlsson","year":"2020","unstructured":"Carlsson G. Topological methods for data modelling. Nat Rev Phys. 2020;2:697\u2013708. https:\/\/doi.org\/10.1038\/s42254-020-00249-3.","journal-title":"Nat Rev Phys"},{"issue":"1","key":"386_CR65","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s41109-019-0179-3","volume":"4","author":"ME Aktas","year":"2019","unstructured":"Aktas ME, Akbas E, Fatmaoui AE. Persistence homology of networks: methods and applications. Appl Netw Sci. 2019;4(1):61. https:\/\/doi.org\/10.1007\/s41109-019-0179-3.","journal-title":"Appl Netw Sci"},{"key":"386_CR66","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.physd.2016.01.002","volume":"323\u2013324","author":"A Sol\u00e9-Ribalta","year":"2016","unstructured":"Sol\u00e9-Ribalta A, De Domenico M, G\u00f3mez S, Arenas A. Random walk centrality in interconnected multilayer networks. Physica D. 2016;323\u2013324:73\u20139. https:\/\/doi.org\/10.1016\/j.physd.2016.01.002.","journal-title":"Physica D"},{"issue":"3","key":"386_CR67","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1527\/tjsai.D-G72","volume":"32","author":"Y Umeda","year":"2017","unstructured":"Umeda Y. Time series classification via topological data analysis. Trans Japanese Soc Artif Intel. 2017;32(3):72\u2013112. https:\/\/doi.org\/10.1527\/tjsai.D-G72.","journal-title":"Trans Japanese Soc Artif Intel"},{"key":"386_CR68","doi-asserted-by":"publisher","unstructured":"Hensel F, Moor M, Rieck B. A survey of topological machine learning methods. Frontiers in Artificial Intelligence 2021;4.https:\/\/doi.org\/10.3389\/frai.2021.681108.","DOI":"10.3389\/frai.2021.681108"},{"key":"386_CR69","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198805090.001.0001","volume-title":"Networks: an introduction","author":"MEJ Newman","year":"2018","unstructured":"Newman MEJ. Networks: an introduction. Oxford: Oxford University Press; 2018."},{"key":"386_CR70","doi-asserted-by":"publisher","unstructured":"Latora V, Marchiori M. Efficient behavior of small-world networks. Physical Review Letters 2001;87(19). https:\/\/doi.org\/10.1103\/physrevlett.87.198701.","DOI":"10.1103\/physrevlett.87.198701"},{"issue":"4","key":"386_CR71","doi-asserted-by":"publisher","first-page":"0123950","DOI":"10.1371\/journal.pone.0123950","volume":"10","author":"ML Stanley","year":"2015","unstructured":"Stanley ML, Simpson SL, Dagenbach D, Lyday RG, Burdette JH, Laurienti PJ. Changes in brain network efficiency and working memory performance in aging. PLoS ONE. 2015;10(4):0123950. https:\/\/doi.org\/10.1371\/journal.pone.0123950.","journal-title":"PLoS ONE"},{"key":"386_CR72","doi-asserted-by":"publisher","unstructured":"Kipf TN, Welling M. Semi-Supervised Classification with Graph Convolutional Networks. arXiv 2016. https:\/\/doi.org\/10.48550\/ARXIV.1609.02907 .","DOI":"10.48550\/ARXIV.1609.02907"},{"key":"386_CR73","doi-asserted-by":"publisher","DOI":"10.48550\/ARXIV.1710.10903","author":"P Veli\u010dkovi\u0107","year":"2017","unstructured":"Veli\u010dkovi\u0107 P, Cucurull G, Casanova A, Romero A, Li\u00f2 P, Bengio Y. Graph attention networks. arXiv. 2017. https:\/\/doi.org\/10.48550\/ARXIV.1710.10903.","journal-title":"arXiv"},{"key":"386_CR74","unstructured":"Xu K, Hu W, Leskovec J, Jegelka S. How powerful are graph neural networks? In: International Conference on Learning Representations 2019. https:\/\/openreview.net\/forum?id=ryGs6iA5Km."},{"key":"386_CR75","first-page":"3844","volume":"29","author":"M Defferrard","year":"2016","unstructured":"Defferrard M, Bresson X, Vandergheynst P. Convolutional neural networks on graphs with fast localized spectral filtering. In: Proceedings of the 30th International Conference on Neural Information Processing Systems NIPS\u201916, Curran Associates Inc, Red Hook, NY, USA. 2016;29:3844\u201352.","journal-title":"In: Proceedings of the 30th International Conference on Neural Information Processing Systems. NIPS\u201916,. Curran Associates Inc., Red Hook, NY, USA"},{"key":"386_CR76","first-page":"1025","volume":"30","author":"WL Hamilton","year":"2017","unstructured":"Hamilton WL, Ying R, Leskovec J. Inductive representation learning on large graphs. In: Proceedings of the 31st International Conference on Neural Information Processing Systems NIPS\u201917 Curran Associates Inc, Red Hook, NY, USA. 2017;30:1025\u201335.","journal-title":"In: Proceedings of the 31st International Conference on Neural Information Processing Systems. NIPS\u201917. Curran Associates Inc., Red Hook, NY, USA"},{"key":"386_CR77","doi-asserted-by":"publisher","first-page":"20172","DOI":"10.1038\/s41598-019-56806-z","volume":"9","author":"E Solana","year":"2019","unstructured":"Solana E, Martinez-Heras E, Casas-Roma J, Calvet L, Lopez-Soley E, Sepulveda M, et al. Modified connectivity of vulnerable brain nodes in multiple sclerosis, their impact on cognition and their discriminative value. Sci Rep. 2019;9:20172. https:\/\/doi.org\/10.1038\/s41598-019-56806-z.","journal-title":"Sci Rep"},{"issue":"5","key":"386_CR78","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1053\/j.sult.2021.07.006","volume":"42","author":"E Martinez-Heras","year":"2021","unstructured":"Martinez-Heras E, Grussu F, Prados F, Solana E, Llufriu S. Diffusion-weighted imaging: Recent advances and applications. Seminars in Ultrasound CT and MRI. 2021;42(5):490\u2013506. https:\/\/doi.org\/10.1053\/j.sult.2021.07.006.","journal-title":"Seminars in Ultrasound CT and MRI"},{"key":"386_CR79","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2013\/671730","volume":"2013","author":"E Sbardella","year":"2013","unstructured":"Sbardella E, Tona F, Petsas N, Pantano P. Dti measurements in multiple sclerosis: evaluation of brain damage and clinical implications. Multiple Sclerosis Int. 2013;2013:1\u201311. https:\/\/doi.org\/10.1155\/2013\/671730.","journal-title":"Multiple Sclerosis Int"},{"key":"386_CR80","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2025.103570","volume":"103","author":"G Qu","year":"2025","unstructured":"Qu G, Zhou Z, Calhoun VD, Zhang A, Wang Y-P. Integrated brain connectivity analysis with fmri, dti, and smri powered by interpretable graph neural networks. Med Image Anal. 2025;103:103570. https:\/\/doi.org\/10.1016\/j.media.2025.103570.","journal-title":"Med Image Anal"}],"container-title":["Health Information Science and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13755-025-00386-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13755-025-00386-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13755-025-00386-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T09:09:33Z","timestamp":1765444173000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13755-025-00386-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,19]]},"references-count":80,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["386"],"URL":"https:\/\/doi.org\/10.1007\/s13755-025-00386-y","relation":{},"ISSN":["2047-2501"],"issn-type":[{"type":"electronic","value":"2047-2501"}],"subject":[],"published":{"date-parts":[[2025,10,19]]},"assertion":[{"value":"30 July 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 October 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Approval was obtained from the ethics committee of MS Center of the University of Naples \u201cFederico II\u201d. The procedures used in this study adhere to the tenets of the Declaration of Helsinki.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}],"article-number":"68"}}