Application of Graph Theory for Identifying Connectivity Patterns in Human Brain Networks: A Systematic Review

Background: Analysis of the human connectome using functional magnetic resonance imaging (fMRI) started in the mid-1990s and attracted increasing attention in attempts to discover the neural underpinnings of human cognition and neurological disorders. In general, brain connectivity patterns from fMRI data are classified as statistical dependencies (functional connectivity) or causal interactions (effective connectivity) among various neural units. Computational methods, especially graph theory-based methods, have recently played a significant role in understanding brain connectivity architecture. Objectives: Thanks to the emergence of graph theoretical analysis, the main purpose of the current paper is to systematically review how brain properties can emerge through the interactions of distinct neuronal units in various cognitive and neurological applications using fMRI. Moreover, this article provides an overview of the existing functional and effective connectivity methods used to construct the brain network, along with their advantages and pitfalls. Methods: In this systematic review, the databases Science Direct, Scopus, arXiv, Google Scholar, IEEE Xplore, PsycINFO, PubMed, and SpringerLink are employed for exploring the evolution of computational methods in human brain connectivity from 1990 to the present, focusing on graph theory. The Cochrane Collaboration's tool was used to assess the risk of bias in individual studies. Results: Our results show that graph theory and its implications in cognitive neuroscience have attracted the attention of researchers since 2009 (as the Human Connectome Project launched), because of their prominent capability in characterizing the behavior of complex brain systems. Although graph theoretical approach can be generally applied to either functional or effective connectivity patterns during rest or task performance, to date, most articles have focused on the resting-state functional connectivity. Conclusions: This review provides an insight into how to utilize graph theoretical measures to make neurobiological inferences regarding the mechanisms underlying human cognition and behavior as well as different brain disorders.

[1]  S. Hanson,et al.  Differences in atypical resting-state effective connectivity distinguish autism from schizophrenia , 2018, NeuroImage: Clinical.

[2]  G. Glover,et al.  Functional neuroanatomy of visuo‐spatial working memory in turner syndrome , 2001, Human brain mapping.

[3]  Yong He,et al.  Graph theoretical modeling of brain connectivity. , 2010, Current opinion in neurology.

[4]  Thomas Nowotny,et al.  Influence of Wiring Cost on the Large-Scale Architecture of Human Cortical Connectivity , 2014, PLoS Comput. Biol..

[5]  L. Pessoa.  Understanding brain networks and brain organization. , 2014, Physics of life reviews.

[6]  M. Breakspear,et al.  The connectomics of brain disorders , 2015, Nature Reviews Neuroscience.

[7]  Karl J. Friston,et al.  A systematic framework for functional connectivity measures , 2014, Front. Neurosci..

[8]  A. Strafella,et al.  Dynamic functional connectivity in Parkinson's disease patients with mild cognitive impairment and normal cognition , 2017, NeuroImage: Clinical.

[9]  H. Pollard,et al.  Network science and the human brain: Using graph theory to understand the brain and one of its hubs, the amygdala, in health and disease , 2016, Journal of neuroscience research.

[10]  John W. Fisher,et al.  Analysis of Functional MRI Data Using Mutual Information , 1999, MICCAI.

[11]  Juan Li,et al.  A new dynamic Bayesian network approach for determining effective connectivity from fMRI data , 2013, Neural Computing and Applications.

[12]  M. P. van den Heuvel,et al.  Normalized Cut Group Clustering of Resting-State fMRI Data , 2008, PloS one.

[13]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[14]  Yu Chen,et al.  The effects of a mid-task break on the brain connectome in healthy participants: A resting-state functional MRI study , 2017, NeuroImage.

[15]  Anil K. Seth,et al.  Granger causality , 2007, Scholarpedia.

[16]  Yong He,et al.  Probabilistic Diffusion Tractography and Graph Theory Analysis Reveal Abnormal White Matter Structural Connectivity Networks in Drug-Naive Boys with Attention Deficit/Hyperactivity Disorder , 2013, The Journal of Neuroscience.

[17]  Vince D. Calhoun,et al.  Aberrant Dynamic Functional Network Connectivity and Graph Properties in Major Depressive Disorder , 2018, Front. Psychiatry.

[18]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[19]  Jonathan D. Power,et al.  Evidence for Hubs in Human Functional Brain Networks , 2013, Neuron.

[20]  A. Zalesky,et al.  Competitive and cooperative dynamics of large-scale brain functional networks supporting recollection , 2012, Proceedings of the National Academy of Sciences.

[21]  S. Rombouts,et al.  Loss of ‘Small-World’ Networks in Alzheimer's Disease: Graph Analysis of fMRI Resting-State Functional Connectivity , 2010, PloS one.

[22]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[23]  Robert Zivadinov,et al.  Clinical significance of atrophy and white matter mean diffusivity within the thalamus of multiple sclerosis patients , 2013, Multiple sclerosis.

[24]  D. Le Bihan,et al.  Diffusion tensor imaging: Concepts and applications , 2001, Journal of magnetic resonance imaging : JMRI.

[25]  Xi-Nian Zuo,et al.  Shared and Distinct Intrinsic Functional Network Centrality in Autism and Attention-Deficit/Hyperactivity Disorder , 2013, Biological Psychiatry.

[26]  Karl J. Friston,et al.  Dynamic causal modelling of electrographic seizure activity using Bayesian belief updating , 2016, NeuroImage.

[27]  Balaram Das,et al.  Generating Conditional Probabilities for Bayesian Networks: Easing the Knowledge Acquisition Problem , 2004, ArXiv.

[28]  Ulrike Basten,et al.  Intelligence is associated with the modular structure of intrinsic brain networks , 2017, Scientific Reports.

[29]  O. Sporns.  Structure and function of complex brain networks , 2013, Dialogues in clinical neuroscience.

[30]  R Baumgartner,et al.  Comparison of two exploratory data analysis methods for fMRI: fuzzy clustering vs. principal component analysis. , 2000, Magnetic resonance imaging.

[31]  J. Mazziotta,et al.  Positron emission tomography study of human brain functional development , 1987, Annals of neurology.

[32]  Erkki Oja,et al.  Independent component analysis: algorithms and applications , 2000, Neural Networks.

[33]  Daniel P. Kennedy,et al.  The Autism Brain Imaging Data Exchange: Towards Large-Scale Evaluation of the Intrinsic Brain Architecture in Autism , 2013, Molecular Psychiatry.

[34]  Yong He,et al.  Topologically Reorganized Connectivity Architecture of Default-Mode, Executive-Control, and Salience Networks across Working Memory Task Loads. , 2016, Cerebral cortex.

[35]  Jonathan D. Power,et al.  Multi-task connectivity reveals flexible hubs for adaptive task control , 2013, Nature Neuroscience.

[36]  M Filippi,et al.  Magnetic resonance techniques to quantify tissue damage, tissue repair, and functional cortical reorganization in multiple sclerosis. , 2009, Progress in brain research.

[37]  G. Buzsáki,et al.  Hippocampal CA1 interneurons: an in vivo intracellular labeling study , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[38]  Karl J. Friston,et al.  Ten simple rules for dynamic causal modeling , 2010, NeuroImage.

[39]  Alan C. Evans,et al.  Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. , 2007, Cerebral cortex.

[40]  Sophie Achard,et al.  Depletion of brain functional connectivity enhancement leads to disability progression in multiple sclerosis: A longitudinal resting-state fMRI study , 2016, Multiple sclerosis.

[41]  D. Yao,et al.  Functional Integration between Salience and Central Executive Networks: A Role for Action Video Game Experience , 2016, Neural plasticity.

[42]  Alan C. Evans,et al.  A Three-Dimensional Statistical Analysis for CBF Activation Studies in Human Brain , 1992, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[43]  Deepti R. Bathula,et al.  Atypical Default Network Connectivity in Youth with Attention-Deficit/Hyperactivity Disorder , 2010, Biological Psychiatry.

[44]  D. Geschwind,et al.  Disentangling the heterogeneity of autism spectrum disorder through genetic findings , 2014, Nature Reviews Neurology.

[45]  M. Chun,et al.  Functional connectome fingerprinting: Identifying individuals based on patterns of brain connectivity , 2015, Nature Neuroscience.

[46]  J. Rapoport,et al.  Simple models of human brain functional networks , 2012, Proceedings of the National Academy of Sciences.

[47]  Yong He,et al.  Imaging Functional and Structural Brain Connectomics in Attention-Deficit/Hyperactivity Disorder , 2014, Molecular Neurobiology.

[48]  G. Frisoni,et al.  Functional network disruption in the degenerative dementias , 2011, The Lancet Neurology.

[49]  Mahdi Jalili,et al.  Graph theoretical analysis of Alzheimer's disease: Discrimination of AD patients from healthy subjects , 2017, Inf. Sci..

[50]  Olaf Sporns,et al.  What Is the Human Connectome , 2009 .

[51]  Paul J. Laurienti,et al.  Defining nodes in complex brain networks , 2013, Front. Comput. Neurosci..

[52]  M. Filippi,et al.  Impaired functional integration in multiple sclerosis: a graph theory study , 2014, Brain Structure and Function.

[53]  Juan Zhou,et al.  Learning effective brain connectivity with dynamic Bayesian networks , 2007, NeuroImage.

[54]  P. Thiran,et al.  Mapping Human Whole-Brain Structural Networks with Diffusion MRI , 2007, PloS one.

[55]  C. Stam.  Modern network science of neurological disorders , 2014, Nature Reviews Neuroscience.

[56]  Paul J. Laurienti,et al.  Comparison of characteristics between region-and voxel-based network analyses in resting-state fMRI data , 2010, NeuroImage.

[57]  Yunyun Duan,et al.  Disrupted topological organization of structural and functional brain connectomes in clinically isolated syndrome and multiple sclerosis , 2016, Scientific Reports.

[58]  Carl D. Hacker,et al.  Clustering of Resting State Networks , 2012, PloS one.

[59]  Yong He,et al.  Identifying and Mapping Connectivity Patterns of Brain Network Hubs in Alzheimer's Disease. , 2015, Cerebral cortex.

[60]  Karl J. Friston,et al.  Statistical parametric maps in functional imaging: A general linear approach , 1994 .

[61]  Alan C. Evans,et al.  Uncovering Intrinsic Modular Organization of Spontaneous Brain Activity in Humans , 2009, PloS one.

[62]  Karl J. Friston.  Functional and Effective Connectivity: A Review , 2011, Brain Connect..

[63]  Damien A. Fair,et al.  Development of large-scale functional networks from birth to adulthood: A guide to the neuroimaging literature , 2017, NeuroImage.

[64]  O Sporns,et al.  Predicting human resting-state functional connectivity from structural connectivity , 2009, Proceedings of the National Academy of Sciences.

[65]  O. Sporns,et al.  Organization, development and function of complex brain networks , 2004, Trends in Cognitive Sciences.

[66]  Vadas Gintautas,et al.  Identification of functional information subgraphs in cultured neural networks , 2009, BMC Neuroscience.

[67]  Mark W. Woolrich,et al.  Network modelling methods for FMRI , 2011, NeuroImage.

[68]  Danielle S. Bassett,et al.  Cognitive Network Neuroscience , 2015, Journal of Cognitive Neuroscience.

[69]  Alan L. Yuille,et al.  Performance comparison of machine learning algorithms and number of independent components used in fMRI decoding of belief vs. disbelief , 2011, NeuroImage.

[70]  S. Petersen,et al.  Characterizing the Hemodynamic Response: Effects of Presentation Rate, Sampling Procedure, and the Possibility of Ordering Brain Activity Based on Relative Timing , 2000, NeuroImage.

[71]  Karl J. Friston,et al.  Structural and Functional Brain Networks: From Connections to Cognition , 2013, Science.

[72]  Nick C Fox,et al.  The Diagnosis of Mild Cognitive Impairment due to Alzheimer’s Disease: Recommendations from the National Institute on Aging-Alzheimer’s Association Workgroups on Diagnostic Guidelines for Alzheimer’s Disease , 2011 .

[73]  C. Wold,et al.  Developmental and autism screening through 2-1-1: reaching underserved families. , 2012, American journal of preventive medicine.

[74]  Jonas Richiardi,et al.  Graph analysis of functional brain networks: practical issues in translational neuroscience , 2014, Philosophical Transactions of the Royal Society B: Biological Sciences.

[75]  Muhammad A. Rushdi,et al.  Schizophrenic patient identification using graph-theoretic features of resting-state fMRI data , 2018, Biomed. Signal Process. Control..

[76]  Mohammad Hossein Fazel Zarandi,et al.  Lung nodule diagnosis from CT images based on ensemble learning , 2015, 2015 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB).

[77]  Alan C. Evans,et al.  Comparing functional connectivity via thresholding correlations and singular value decomposition , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[78]  Junjing Wang,et al.  Graph theoretical analysis reveals disrupted topological properties of whole brain functional networks in temporal lobe epilepsy , 2014, Clinical Neurophysiology.

[79]  Marina Vannucci,et al.  Bayesian models for functional magnetic resonance imaging data analysis , 2014 .

[80]  Yong He,et al.  Understanding Structural-Functional Relationships in the Human Brain , 2015, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[81]  A. Kraskov,et al.  Estimating mutual information. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[82]  F. Vecchio,et al.  Connectome: Graph theory application in functional brain network architecture , 2017, Clinical neurophysiology practice.

[83]  O. Sporns,et al.  The economy of brain network organization , 2012, Nature Reviews Neuroscience.

[84]  Ahmed Ben Hamida,et al.  The Influence of Preprocessing Steps on Graph Theory Measures Derived from Resting State fMRI , 2018, Front. Comput. Neurosci..

[85]  Mingzhou Ding,et al.  Is Granger Causality a Viable Technique for Analyzing fMRI Data? , 2013, PloS one.

[86]  B. Pakkenberg,et al.  Aging and the human neocortex , 2003, Experimental Gerontology.

[87]  Giovanni Rizzo,et al.  Brain functional connectivity in sleep-related hypermotor epilepsy , 2017, NeuroImage: Clinical.

[88]  J. Pekar,et al.  A method for making group inferences from functional MRI data using independent component analysis , 2001, Human brain mapping.

[89]  Mohammad Reza Daliri,et al.  Altered topological properties of brain networks in the early MS patients revealed by cognitive task-related fMRI and graph theory , 2018, Biomed. Signal Process. Control..

[90]  Lorena R. R. Gianotti,et al.  Functional brain network efficiency predicts intelligence , 2012, Human brain mapping.

[91]  B. T. Thomas Yeo,et al.  Proportional thresholding in resting-state fMRI functional connectivity networks and consequences for patient-control connectome studies: Issues and recommendations , 2017, NeuroImage.

[92]  Bin He,et al.  A weighted small world network measure for assessing functional connectivity , 2013, Journal of Neuroscience Methods.

[93]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[94]  Q. Gong,et al.  Depression, Neuroimaging and Connectomics: A Selective Overview , 2015, Biological Psychiatry.

[95]  Klaas E. Stephan,et al.  Dynamic causal modelling: A critical review of the biophysical and statistical foundations , 2011, NeuroImage.

[96]  Olaf Sporns,et al.  The human connectome: Origins and challenges , 2013, NeuroImage.

[97]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[98]  Athanasios V. Vasilakos,et al.  Small-world human brain networks: Perspectives and challenges , 2017, Neuroscience & Biobehavioral Reviews.

[99]  Xiao Yang,et al.  Altered topological patterns of large-scale brain functional networks during passive hyperthermia , 2013, Brain and Cognition.

[100]  Daniel L. Rubin,et al.  Network Analysis of Intrinsic Functional Brain Connectivity in Alzheimer's Disease , 2008, PLoS Comput. Biol..

[101]  Vinod Menon,et al.  Functional connectivity in the resting brain: A network analysis of the default mode hypothesis , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[102]  E. DeYoe,et al.  Analysis and use of FMRI response delays , 2001, Human brain mapping.

[103]  Anna Manelis,et al.  Anticipation-related brain connectivity in bipolar and unipolar depression: a graph theory approach. , 2016, Brain : a journal of neurology.

[104]  Ranjana K. Mehta,et al.  Neuroergonomics: a review of applications to physical and cognitive work , 2013, Front. Hum. Neurosci..

[105]  D. Shi,et al.  Disrupted brain network topology in chronic insomnia disorder: A resting-state fMRI study , 2018, NeuroImage: Clinical.

[106]  B. Biswal,et al.  Characterizing variation in the functional connectome: promise and pitfalls , 2012, Trends in Cognitive Sciences.

[107]  R. Haier,et al.  The Parieto-Frontal Integration Theory (P-FIT) of intelligence: Converging neuroimaging evidence , 2007, Behavioral and Brain Sciences.

[108]  Takashi Yamada,et al.  Altered Network Topologies and Hub Organization in Adults with Autism: A Resting-State fMRI Study , 2014, PloS one.

[109]  Stephen M. Smith,et al.  Probabilistic independent component analysis for functional magnetic resonance imaging , 2004, IEEE Transactions on Medical Imaging.

[110]  C. Keown,et al.  Network organization is globally atypical in autism: A graph theory study of intrinsic functional connectivity. , 2017, Biological psychiatry. Cognitive neuroscience and neuroimaging.

[111]  Qiang Ji,et al.  Knowledge Based Activity Recognition with Dynamic Bayesian Network , 2010, ECCV.

[112]  Dante R Chialvo,et al.  Identifying directed links in large scale functional networks: application to brain fMRI , 2007, BMC Cell Biology.

[113]  S. Petersen,et al.  Brain Networks and Cognitive Architectures , 2015, Neuron.

[114]  Olaf Sporns,et al.  Network attributes for segregation and integration in the human brain , 2013, Current Opinion in Neurobiology.

[115]  Amirali Kazeminejad,et al.  Topological Properties of Resting-State fMRI Functional Networks Improve Machine Learning-Based Autism Classification , 2019, Front. Neurosci..

[116]  Keith Heberlein,et al.  Imaging human connectomes at the macroscale , 2013, Nature Methods.

[117]  T. Prescott,et al.  The brainstem reticular formation is a small-world, not scale-free, network , 2006, Proceedings of the Royal Society B: Biological Sciences.

[118]  Adriana Galván,et al.  The use of functional and effective connectivity techniques to understand the developing brain , 2015, Developmental Cognitive Neuroscience.

[119]  Graeme D. Jackson,et al.  Increased segregation of brain networks in focal epilepsy: An fMRI graph theory finding , 2015, NeuroImage: Clinical.

[120]  Yong He,et al.  Graph-based network analysis of resting-state functional MRI. , 2010 .

[121]  Kaiming Li,et al.  Review of methods for functional brain connectivity detection using fMRI , 2009, Comput. Medical Imaging Graph..

[122]  U. Ziemann,et al.  Working memory performance of early MS patients correlates inversely with modularity increases in resting state functional connectivity networks , 2014, NeuroImage.

[123]  Santanu Chaudhury,et al.  Learning effective connectivity from fMRI using autoregressive hidden Markov model with missing data , 2017, Journal of Neuroscience Methods.

[124]  Kathryn R. Cullen,et al.  Network analysis of functional brain connectivity in borderline personality disorder using resting-state fMRI , 2016, NeuroImage: Clinical.

[125]  Nir Friedman,et al.  Bayesian Network Classifiers , 1997, Machine Learning.

[126]  Kuncheng Li,et al.  Functional Brain Network Alterations in Clinically Isolated Syndrome and Multiple Sclerosis: A Graph-based Connectome Study. , 2017, Radiology.

[127]  Menno M. Schoonheim,et al.  Network Collapse and Cognitive Impairment in Multiple Sclerosis , 2015, Front. Neurol..

[128]  G. Sandini,et al.  Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer's disease. , 2009, Brain : a journal of neurology.

[129]  Dietmar Cordes,et al.  Hierarchical clustering to measure connectivity in fMRI resting-state data. , 2002, Magnetic resonance imaging.

[130]  Sophie Achard,et al.  Nodal approach reveals differential impact of lateralized focal epilepsies on hub reorganization , 2015, NeuroImage.

[131]  X Hu,et al.  Analysis of functional magnetic resonance imaging data using self‐organizing mapping with spatial connectivity , 1999, Magnetic resonance in medicine.

[132]  Steven L. Bressler,et al.  Wiener–Granger Causality: A well established methodology , 2011, NeuroImage.

[133]  R. Peterson,et al.  Mild cognitive impairment: Transition from aging to Alzheimer's disease , 2000, Neurobiology of Aging.

[134]  H. Berendse,et al.  The application of graph theoretical analysis to complex networks in the brain , 2007, Clinical Neurophysiology.

[135]  Richard F. Betzel,et al.  Modular Brain Networks. , 2016, Annual review of psychology.

[136]  Mohammad Hossein Fazel Zarandi,et al.  Hybrid intelligent approach for diagnosis of the lung nodule from CT images using spatial kernelized fuzzy c-means and ensemble learning , 2018, Math. Comput. Simul..

[137]  Sepideh Sadaghiani,et al.  Ongoing dynamics in large-scale functional connectivity predict perception , 2015, Proceedings of the National Academy of Sciences.

[138]  Olaf Sporns,et al.  Communication dynamics in complex brain networks , 2017, Nature Reviews Neuroscience.

[139]  F. L. D. Silva,et al.  Event-related EEG/MEG synchronization and desynchronization: basic principles , 1999, Clinical Neurophysiology.

[140]  Z. Haneef,et al.  Graph theory findings in the pathophysiology of temporal lobe epilepsy , 2014, Clinical Neurophysiology.

[141]  Karl J. Friston.  Functional and effective connectivity in neuroimaging: A synthesis , 1994 .

[142]  J. Sterne,et al.  The Cochrane Collaboration’s tool for assessing risk of bias in randomised trials , 2011, BMJ : British Medical Journal.

[143]  K. Worsley,et al.  The geometry of correlation fields with an application to functional connectivity of the brain , 1999 .

[144]  Changiz Eslahchi,et al.  Screening of autism based on task-free fMRI using graph theoretical approach , 2017, Psychiatry Research: Neuroimaging.

[145]  E. Bullmore,et al.  Neurophysiological architecture of functional magnetic resonance images of human brain. , 2005, Cerebral cortex.

[146]  O. Sporns,et al.  Network hubs in the human brain , 2013, Trends in Cognitive Sciences.

[147]  Yong He,et al.  Convergence and divergence across construction methods for human brain white matter networks: An assessment based on individual differences , 2015, Human brain mapping.

[148]  Yong He,et al.  Disrupted Functional Brain Connectome in Individuals at Risk for Alzheimer's Disease , 2013, Biological Psychiatry.

[149]  Danielle S Bassett,et al.  Brain graphs: graphical models of the human brain connectome. , 2011, Annual review of clinical psychology.

[150]  A. Seth,et al.  Granger causality and transfer entropy are equivalent for Gaussian variables. , 2009, Physical review letters.

[151]  Alan C. Evans,et al.  Topological Organization of Functional Brain Networks in Healthy Children: Differences in Relation to Age, Sex, and Intelligence , 2013, PloS one.

[152]  Yong He,et al.  Assessment of system dysfunction in the brain through MRI-based connectomics , 2013, The Lancet Neurology.

[153]  P. Boesiger,et al.  A new correlation‐based fuzzy logic clustering algorithm for FMRI , 1998, Magnetic resonance in medicine.

[154]  Andrea Mechelli,et al.  A report of the functional connectivity workshop, Dusseldorf 2002 , 2003, NeuroImage.

[155]  Karl J. Friston.  Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging , 2009, PLoS biology.

[156]  Mohammad Hossein Fazel Zarandi,et al.  Proposing a model for operating room scheduling based on fuzzy surgical duration , 2016, 2016 Annual Conference of the North American Fuzzy Information Processing Society (NAFIPS).

[157]  Li Yao,et al.  Effective connectivity analysis of default mode network based on the Bayesian network learning approach , 2009, Medical Imaging.

[158]  Danielle Smith Bassett,et al.  Small-World Brain Networks , 2006, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[159]  David Rose,et al.  Topological Properties , 2022 .

[160]  Olaf Sporns,et al.  The Human Connectome: A Structural Description of the Human Brain , 2005, PLoS Comput. Biol..

[161]  Ruth Ann Marrie,et al.  Comorbidity in multiple sclerosis: implications for patient care , 2017, Nature Reviews Neurology.

[162]  D. Yao,et al.  Altered basal ganglia-cortical functional connections in frontal lobe epilepsy: A resting-state fMRI study , 2016, Epilepsy Research.

[163]  Frederik Barkhof,et al.  Increased default-mode network centrality in cognitively impaired multiple sclerosis patients , 2017, Neurology.

[164]  Mukesh Jain,et al.  A next-generation approach to the characterization of a non-model plant transcriptome * , 2011 .

[165]  Jyotsna Nair,et al.  Clinical review: evidence-based diagnosis and treatment of ADHD in children. , 2006, Missouri medicine.

[166]  Alan C. Evans,et al.  Multi-level bootstrap analysis of stable clusters in resting-state fMRI , 2009, NeuroImage.

[167]  A. Seth,et al.  Granger Causality Analysis in Neuroscience and Neuroimaging , 2015, The Journal of Neuroscience.

[168]  F. Gonzalez-Lima,et al.  Structural equation modeling and its application to network analysis in functional brain imaging , 1994 .

[169]  J. Shimony,et al.  Resting-State fMRI: A Review of Methods and Clinical Applications , 2013, American Journal of Neuroradiology.

[170]  Sergey Borisov,et al.  Large-scale brain functional modularity is reflected in slow electroencephalographic rhythms across the human non-rapid eye movement sleep cycle , 2013, NeuroImage.

[171]  Jonathan D. Power,et al.  Functional Brain Networks Develop from a “Local to Distributed” Organization , 2009, PLoS Comput. Biol..

[172]  Jesse A. Brown,et al.  Altered functional and structural brain network organization in autism☆ , 2012, NeuroImage: Clinical.

[173]  E. Fava.  Sensation & Perception , 2004, NeuroImage.

[174]  C. Beste,et al.  On the role of the prefrontal cortex in fatigue effects on cognitive flexibility - a system neurophysiological approach , 2018, Scientific Reports.

[175]  A. Bezerianos,et al.  Functional cortical connectivity analysis of mental fatigue unmasks hemispheric asymmetry and changes in small-world networks , 2014, Brain and Cognition.

[176]  D. Moher,et al.  Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement. , 2010, International journal of surgery.

[177]  Manuel Schabus,et al.  Hierarchical clustering of brain activity during human nonrapid eye movement sleep , 2012, Proceedings of the National Academy of Sciences.

[178]  Alan L. Yuille,et al.  Non-negative matrix factorization of multimodal MRI, fMRI and phenotypic data reveals differential changes in default mode subnetworks in ADHD , 2014, NeuroImage.

[179]  Cornelis J. Stam,et al.  Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain , 2008, NeuroImage.

[180]  V. Calhoun,et al.  Aberrant Functional Whole-Brain Network Architecture in Patients With Schizophrenia: A Meta-analysis. , 2016, Schizophrenia bulletin.

[181]  Edward T. Bullmore,et al.  Modular and Hierarchically Modular Organization of Brain Networks , 2010, Front. Neurosci..

[182]  Waldemar Karwowski,et al.  Computational Methods for Analyzing Functional and Effective Brain Network Connectivity Using fMRI , 2018, Advances in Neuroergonomics and Cognitive Engineering.

[183]  J. Levitt,et al.  Static and dynamic posterior cingulate cortex nodal topology of default mode network predicts attention task performance , 2015, Brain Imaging and Behavior.

[184]  M. Catani,et al.  The rises and falls of disconnection syndromes. , 2005, Brain : a journal of neurology.

[185]  H. Lagercrantz,et al.  The functional architecture of the infant brain as revealed by resting-state fMRI. , 2011, Cerebral cortex.

[186]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[187]  R. Benedict,et al.  The thalamus and multiple sclerosis , 2013, Neurology.

[188]  Jane R. Allison,et al.  A Relationship between the Transient Structure in the Monomeric State and the Aggregation Propensities of α-Synuclein and β-Synuclein , 2014, Biochemistry.

[189]  Piet Van Mieghem,et al.  Assortativity in complex networks , 2015, J. Complex Networks.

[190]  Luca Faes,et al.  MuTE: A MATLAB Toolbox to Compare Established and Novel Estimators of the Multivariate Transfer Entropy , 2014, PloS one.

[191]  M. Fox,et al.  Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging , 2007, Nature Reviews Neuroscience.

[192]  J. Guilford,et al.  The nature of human intelligence. , 1968 .

[193]  William D. Penny,et al.  Comparing Dynamic Causal Models using AIC, BIC and Free Energy , 2012, NeuroImage.

[194]  Mark W. Woolrich,et al.  The danger of systematic bias in group-level FMRI-lag-based causality estimation , 2012, NeuroImage.

[195]  Francesca Baglio,et al.  Exploring resting-state functional connectivity invariants across the lifespan in healthy people by means of a recently proposed graph theoretical model , 2018, PloS one.

[196]  Steen Moeller,et al.  The Human Connectome Project: A data acquisition perspective , 2012, NeuroImage.

[197]  Olaf Sporns,et al.  Graph theory methods: applications in brain networks , 2018, Dialogues in clinical neuroscience.

[198]  Yong He,et al.  Topological organization of the human brain functional connectome across the lifespan , 2013, Developmental Cognitive Neuroscience.

[199]  N. Tzourio-Mazoyer,et al.  Automated Anatomical Labeling of Activations in SPM Using a Macroscopic Anatomical Parcellation of the MNI MRI Single-Subject Brain , 2002, NeuroImage.

[200]  K. Gurney,et al.  Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence , 2008, PloS one.

[201]  Frederico A. C. Azevedo,et al.  Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled‐up primate brain , 2009, The Journal of comparative neurology.

[202]  N. Volkow,et al.  Abnormal Functional Connectivity in Children with Attention-Deficit/Hyperactivity Disorder , 2012, Biological Psychiatry.

[203]  Lisa E. Mash,et al.  Multimodal approaches to functional connectivity in autism spectrum disorders: An integrative perspective , 2018, Developmental neurobiology.

[204]  Arjan Hillebrand,et al.  Functional brain networks: Linking thalamic atrophy to clinical disability in multiple sclerosis, a multimodal fMRI and MEG Study , 2015, Human brain mapping.

[205]  Qiang Shen,et al.  Learning Bayesian networks: approaches and issues , 2011, The Knowledge Engineering Review.

[206]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[207]  M. V. D. Heuvel,et al.  Exploring the brain network: A review on resting-state fMRI functional connectivity , 2010, European Neuropsychopharmacology.

[208]  Mingzhou Ding,et al.  Analyzing information flow in brain networks with nonparametric Granger causality , 2008, NeuroImage.

[209]  Sarah Feldt Muldoon,et al.  Small-World Propensity and Weighted Brain Networks , 2016, Scientific Reports.

[210]  Timothy O. Laumann,et al.  Functional Network Organization of the Human Brain , 2011, Neuron.

[211]  Joaquín Goñi,et al.  Changes in structural and functional connectivity among resting-state networks across the human lifespan , 2014, NeuroImage.

[212]  W. Kuo,et al.  Increasing fMRI Sampling Rate Improves Granger Causality Estimates , 2014, PloS one.

[213]  Karl J. Friston,et al.  Analysis of functional MRI time‐series , 1994, Human Brain Mapping.

[214]  Paul J. Laurienti,et al.  The Ubiquity of Small-World Networks , 2011, Brain Connect..

[215]  R. Kahn,et al.  Efficiency of Functional Brain Networks and Intellectual Performance , 2009, The Journal of Neuroscience.

[216]  Markus Lappe,et al.  Time-Delayed Mutual Information of the Phase as a Measure of Functional Connectivity , 2012, PloS one.

[217]  Christian Montag,et al.  Working memory capacity and the functional connectome - insights from resting-state fMRI and voxelwise centrality mapping , 2018, Brain Imaging and Behavior.

[218]  J. Xiong,et al.  Detecting functional connectivity in the resting brain: a comparison between ICA and CCA. , 2007, Magnetic resonance imaging.

[219]  M. Mesulam,et al.  From sensation to cognition. , 1998, Brain : a journal of neurology.

[220]  Anil K. Seth,et al.  A MATLAB toolbox for Granger causal connectivity analysis , 2010, Journal of Neuroscience Methods.

[221]  Moo K. Chung,et al.  Multi-resolution statistical analysis of brain connectivity graphs in preclinical Alzheimer's disease , 2015, NeuroImage.

[222]  Edward T. Bullmore,et al.  Age-related changes in modular organization of human brain functional networks , 2009, NeuroImage.

[223]  R. Malach,et al.  Data-driven clustering reveals a fundamental subdivision of the human cortex into two global systems , 2008, Neuropsychologia.

[224]  Mark W. Woolrich,et al.  Resting-state fMRI in the Human Connectome Project , 2013, NeuroImage.

[225]  O. Sporns,et al.  Network centrality in the human functional connectome. , 2012, Cerebral cortex.

[226]  Scott T. Grafton,et al.  Dynamic reconfiguration of human brain networks during learning , 2010, Proceedings of the National Academy of Sciences.

[227]  Olaf Sporns,et al.  Complex network measures of brain connectivity: Uses and interpretations , 2010, NeuroImage.

[228]  Thomas E. Nichols,et al.  Subcortical brain volume differences in participants with attention deficit hyperactivity disorder in children and adults: a cross-sectional mega-analysis. , 2017, The lancet. Psychiatry.

[229]  Cornelis J. Stam,et al.  Disrupted modular brain dynamics reflect cognitive dysfunction in Alzheimer's disease , 2012, NeuroImage.

[230]  Yong He,et al.  Toward Developmental Connectomics of the Human Brain , 2016, Front. Neuroanat..

[231]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[232]  Nikolaus Kriegeskorte,et al.  Cognitive computational neuroscience , 2018, Nature Neuroscience.

[233]  Rainer Goebel,et al.  The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution , 2011, NeuroImage.

[234]  L. Waller,et al.  GraphVar 2.0: A user-friendly toolbox for machine learning on functional connectivity measures , 2018, Journal of Neuroscience Methods.

[235]  F. Valldeoriola,et al.  Discriminating cognitive status in Parkinson’s disease through functional connectomics and machine learning , 2017, Scientific Reports.

[236]  K. M. Deneen,et al.  Altered effective connectivity patterns of the default mode network in Alzheimer's disease: An fMRI study , 2014, Neuroscience Letters.

[237]  O. Sporns.  Contributions and challenges for network models in cognitive neuroscience , 2014, Nature Neuroscience.

[238]  K. Hwang,et al.  The development of hub architecture in the human functional brain network. , 2013, Cerebral cortex.

[239]  Colin Humphries,et al.  Altered Frontal Lobe Network Function in Temporal Lobe Epilepsy Revealed by Graph Theory Analysis (P1.279) , 2018 .

[240]  Jamie D. Feusner,et al.  Graph-theoretical analysis of resting-state fMRI in pediatric obsessive-compulsive disorder. , 2016, Journal of affective disorders.

[241]  Fumiko Hoeft,et al.  GAT: A Graph-Theoretical Analysis Toolbox for Analyzing Between-Group Differences in Large-Scale Structural and Functional Brain Networks , 2012, PloS one.

[242]  Karl J. Friston,et al.  Functional Connectivity: The Principal-Component Analysis of Large (PET) Data Sets , 1993, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[243]  Jan-Mathijs Schoffelen,et al.  A Tutorial Review of Functional Connectivity Analysis Methods and Their Interpretational Pitfalls , 2016, Front. Syst. Neurosci..

[244]  A. Fagan,et al.  Functional connectivity and graph theory in preclinical Alzheimer's disease , 2014, Neurobiology of Aging.

[245]  Giovanni Volpe,et al.  BRAPH: A graph theory software for the analysis of brain connectivity , 2017, bioRxiv.

[246]  Mingrui Xia,et al.  Magnetic Resonance Imaging and Graph Theoretical Analysis of Complex Brain Networks in Neuropsychiatric Disorders , 2011, Brain Connect..

[247]  João Ricardo Sato,et al.  Decreased centrality of cortical volume covariance networks in autism spectrum disorders. , 2015, Journal of psychiatric research.

[248]  Boris C. Bernhardt,et al.  Network analysis for a network disorder: The emerging role of graph theory in the study of epilepsy , 2015, Epilepsy & Behavior.

[249]  M. Chun,et al.  Functional connectome fingerprinting: Identifying individuals based on patterns of brain connectivity , 2015, Nature Neuroscience.

[250]  Michael Breakspear,et al.  Graph analysis of the human connectome: Promise, progress, and pitfalls , 2013, NeuroImage.

[251]  Paul M. Thompson,et al.  Hemispheric brain asymmetry differences in youths with attention-deficit/hyperactivity disorder , 2018, NeuroImage: Clinical.

[252]  Karl J. Friston,et al.  Detecting Activations in PET and fMRI: Levels of Inference and Power , 1996, NeuroImage.

[253]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[254]  Manfred G Kitzbichler,et al.  Cognitive Effort Drives Workspace Configuration of Human Brain Functional Networks , 2011, The Journal of Neuroscience.

[255]  Hojjat Adeli,et al.  Graph Theory and Brain Connectivity in Alzheimer’s Disease , 2017, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[256]  W. Hauser,et al.  Epilepsy: Frequency Causes and Consequences , 1990 .

[257]  C. Johnson,et al.  Identification and Evaluation of Children With Autism Spectrum Disorders , 2007, Pediatrics.

[258]  Jonathan D. Power,et al.  The Development of Human Functional Brain Networks , 2010, Neuron.

[259]  S. H. Hojjati,et al.  Predicting conversion from MCI to AD using resting-state fMRI, graph theoretical approach and SVM , 2017, Journal of Neuroscience Methods.

[260]  Karl J. Friston,et al.  Comparing Functional (PET) Images: The Assessment of Significant Change , 1991, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[261]  Yong He,et al.  Disrupted structural and functional brain connectomes in mild cognitive impairment and Alzheimer’s disease , 2014, Neuroscience Bulletin.

[262]  Karl J. Friston,et al.  Network discovery with DCM , 2011, NeuroImage.

[263]  Swathi P. Iyer,et al.  Distinct neural signatures detected for ADHD subtypes after controlling for micro-movements in resting state functional connectivity MRI data , 2012, Front. Syst. Neurosci..

[264]  Gordon Pipa,et al.  Transfer entropy—a model-free measure of effective connectivity for the neurosciences , 2010, Journal of Computational Neuroscience.

[265]  I. Rektor,et al.  Large-scale cortico-subcortical functional networks in focal epilepsies: The role of the basal ganglia , 2016, NeuroImage: Clinical.

[266]  Kai-Hsiang Chuang,et al.  Model-free functional MRI analysis using Kohonen clustering neural network and fuzzy C-means , 1999, IEEE Transactions on Medical Imaging.

[267]  S. Spencer,et al.  When should temporal-lobe epilepsy be treated surgically? , 2002, The Lancet Neurology.

[268]  Kai Li,et al.  Computational approaches to fMRI analysis , 2017, Nature Neuroscience.

[269]  Jennifer H. Pfeifer,et al.  Current methods and limitations for longitudinal fMRI analysis across development , 2017, Developmental Cognitive Neuroscience.

[270]  K. Miller.  Executive functions. , 2005, Pediatric annals.

[271]  R. Lenroot,et al.  Heterogeneity within Autism Spectrum Disorders: What have We Learned from Neuroimaging Studies? , 2013, Front. Hum. Neurosci..

[272]  D. Bassett,et al.  Dynamic reconfiguration of frontal brain networks during executive cognition in humans , 2015, Proceedings of the National Academy of Sciences.

[273]  A. Babajani-Feremi,et al.  Application of advanced machine learning methods on resting-state fMRI network for identification of mild cognitive impairment and Alzheimer’s disease , 2015, Brain Imaging and Behavior.

[274]  E. Bullmore,et al.  Human brain networks in health and disease , 2009, Current opinion in neurology.

[275]  Changsong Zhou,et al.  Trade-off between Multiple Constraints Enables Simultaneous Formation of Modules and Hubs in Neural Systems , 2013, PLoS Comput. Biol..

[276]  J. D. Kruschwitz,et al.  GraphVar: A user-friendly toolbox for comprehensive graph analyses of functional brain connectivity , 2015, Journal of Neuroscience Methods.

[277]  Lee M. Miller,et al.  Measuring interregional functional connectivity using coherence and partial coherence analyses of fMRI data , 2004, NeuroImage.

[278]  Juan Zhou,et al.  Applications of Resting-State Functional Connectivity to Neurodegenerative Disease. , 2017, Neuroimaging clinics of North America.

[279]  Karl J. Friston,et al.  Analysing connectivity with Granger causality and dynamic causal modelling , 2013, Current Opinion in Neurobiology.

[280]  W. M. van der Flier,et al.  Functional neural network analysis in frontotemporal dementia and Alzheimer's disease using EEG and graph theory , 2009, BMC Neuroscience.

[281]  Edward T. Bullmore,et al.  Connectomics: A new paradigm for understanding brain disease , 2015, European Neuropsychopharmacology.

[282]  P. Hofman,et al.  Loss of network efficiency associated with cognitive decline in chronic epilepsy , 2011, Neurology.

[283]  Andrew Zalesky,et al.  Altered Functional Brain Connectivity in a Non-Clinical Sample of Young Adults with Attention-Deficit/Hyperactivity Disorder , 2012, The Journal of Neuroscience.

[284]  John D. E. Gabrieli,et al.  Intrinsic functional network organization in high-functioning adolescents with autism spectrum disorder , 2013, Front. Hum. Neurosci..

[285]  Linda Douw,et al.  Task-dependent reorganization of functional connectivity networks during visual semantic decision making , 2014, Brain and behavior.

[286]  E. Juratovac,et al.  Age-Related Changes , 2017 .

[287]  David T. Jones,et al.  Functional Connectivity in Dementia , 2018 .

[288]  Vinzenz Fleischer,et al.  Graph Theoretical Framework of Brain Networks in Multiple Sclerosis: A Review of Concepts , 2017, Neuroscience.

[289]  Aline Viol,et al.  Brain complex network analysis by means of resting state fMRI and graph analysis: Will it be helpful in clinical epilepsy? , 2014, Epilepsy & Behavior.

[290]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[291]  Li Yao,et al.  Age Related Changes in Topological Properties of Brain Functional Network and Structural Connectivity , 2018, Front. Neurosci..

[292]  Mark S. Cohen,et al.  Insights into multimodal imaging classification of ADHD , 2012, Front. Syst. Neurosci..

[293]  Raja Parasuraman,et al.  Neuroergonomics: The Brain at Work , 2006 .

[294]  Lior Rokach,et al.  Clustering Methods , 2005, The Data Mining and Knowledge Discovery Handbook.

[295]  M. Milham,et al.  The ADHD-200 Consortium: A Model to Advance the Translational Potential of Neuroimaging in Clinical Neuroscience , 2012, Front. Syst. Neurosci..

[296]  Russell A. Poldrack,et al.  Six problems for causal inference from fMRI , 2010, NeuroImage.

[297]  F Barkhof,et al.  Changes in functional network centrality underlie cognitive dysfunction and physical disability in multiple sclerosis , 2014, Multiple sclerosis.

[298]  C Ecker,et al.  Translational approaches to the biology of Autism: false dawn or a new era? , 2012, Molecular Psychiatry.

[299]  Edward T. Bullmore,et al.  Schizophrenia, neuroimaging and connectomics , 2012, NeuroImage.

[300]  J. Karbowski.  Optimal wiring principle and plateaus in the degree of separation for cortical neurons. , 2001, Physical review letters.

[301]  Habib Benali,et al.  Characteristics of the default mode functional connectivity in normal ageing and Alzheimer's disease using resting state fMRI with a combined approach of entropy-based and graph theoretical measurements , 2014, NeuroImage.

[302]  Mark S. Cohen,et al.  Single trial decoding of belief decision making from EEG and fMRI data using independent components features , 2013, Front. Hum. Neurosci..

[303]  Kanthaiah Koka,et al.  Assessment of Cochlear Function during Cochlear Implantation by Extra- and Intracochlear Electrocochleography , 2018, Front. Neurosci..

[304]  Scott K. Holland,et al.  Altered functional network connectivity in preterm infants: antecedents of cognitive and motor impairments? , 2018, Brain Structure and Function.

[305]  Abbas Babajani-Feremi,et al.  Identifying patients with Alzheimer’s disease using resting-state fMRI and graph theory , 2015, Clinical Neurophysiology.

[306]  Vadim Ushakov,et al.  Causal Interactions Within the Default Mode Network as Revealed by Low-Frequency Brain Fluctuations and Information Transfer Entropy , 2016 .

[307]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[308]  Paul J. Laurienti,et al.  Changes in Brain Network Efficiency and Working Memory Performance in Aging , 2015, PloS one.

[309]  Xueyu Wang,et al.  Altered degree centrality in childhood absence epilepsy: A resting-state fMRI study , 2017, Journal of the Neurological Sciences.

[310]  D. Tank,et al.  Brain magnetic resonance imaging with contrast dependent on blood oxygenation. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[311]  Liang Wang,et al.  Altered small‐world brain functional networks in children with attention‐deficit/hyperactivity disorder , 2009, Human brain mapping.

[312]  G. J. Fleer,et al.  Stationary dynamics approach to analytical approximations for polymer coexistence curves. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[313]  E. Bullmore,et al.  A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs , 2006, The Journal of Neuroscience.

[314]  M. V. D. Heuvel,et al.  Brain Networks in Schizophrenia , 2014, Neuropsychology Review.

[315]  H. Lüders,et al.  Presurgical evaluation of epilepsy. , 2001, Brain : a journal of neurology.

[316]  Ulrike Basten,et al.  Efficient hubs in the intelligent brain: Nodal efficiency of hub regions in the salience network is associated with general intelligence , 2017 .

[317]  M. Farlow,et al.  Treatment of mild cognitive impairment (MCI). , 2009, Current Alzheimer research.

[318]  Seong-Gi Kim,et al.  Relative changes of cerebral arterial and venous blood volumes during increased cerebral blood flow: Implications for BOLD fMRI , 2001, Magnetic resonance in medicine.

[319]  Dinggang Shen,et al.  Temporal and Spatial Evolution of Brain Network Topology during the First Two Years of Life , 2011, PloS one.