The information content of EEG recordings, which are widely used and important for assessing the functional activity of the brain, is significantly increased by the use of mathematical analysis, where an important place is occupied by the spatial synchronization characteristic, i.e., the functional connectivity of biopotentials (based on correlation and coherence analysis, phase synchronization, etc.). The success of neuroimaging methods in recent years has not only confirmed the significance of this indicator, but has also contributed to improvements in approaches to its statistical evaluation and visualization. Graph theory (GT) is a promising method for analyzing the neural network organization of the brain. Its advantages are that it provides a visual description of the entire structure of the network and its individual components, as well as defining the relationships between them. The purpose of this review is to present approaches to the application of graph theory and the potentials of this method based on the analysis of published data. We present general information on the areas of application of GT, address the most common and informative metrics, and provide recommendations for selecting software. Modifications of GT analysis of the EEG are described: without primary localization of the generation sources of EEG components and with their localization. Examples of the effective use of graph theory analysis of the electroencephalogram of the healthy and diseased brain are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abeyasinghe, P. M., Ribeiro de Paula, D., Khajehabdollahi, S., et al., “Role of dimensionality in predicting the spontaneous behavior of the brain using the classical Ising model and the Ising model implemented on a structural connectome,” Brain Connect., 8, No. 7, 444–455 (2018), https://doi.org/10.1089/brain.2017.0516.
Adamovich, T. V., “Integration and segregation in the functional networks of the brain,” Teor. Eksperim. Psikhol., 13, No, 3, 1–25 (2020).
Anokhin, K. V., “The cognitome in searches for a fundamental theory of consciousness,” Zh. Vyssh. Nerv. Deyat., 71, No, 1, 39–71 (2021), https://doi.org/10.31857/S0044467721010032.
Arnatkevičiūtė, A., Fulcher, B. D., Pocock, R., and Fornito, A., “Hub connectivity, neuronal diversity, and gene expression in the Caenorhabditis elegans connectome,” PLoS Comput. Biol., 14, No, 2, 1–32 (2018), https://doi.org/10.1371/journal.pcbi.1005989.
Avena-Koenigsberger, A., Misic, B., and Sporns, O., “Communication dynamics in complex brain networks,” Nat. Rev. Neurosci., 19, No, 1, 17–33 (2018).
Awan, F. G., Saleem, O., and Kiran, A., “Recent trends and advances in solving the inverse problem for EEG source localization,” Inverse Probl. Sci. Eng., 27, No, 11, 1521–1536 (2019).
Babiloni, C., Blinowska, K., Bonanni, L., et al., “What electrophysiology tells us about Alzheimer’s disease: A window into the synchronization and connectivity of brain neurons,” Neurobiol. Aging, 85, 58–73 (2020), https://doi.org/10.1016/j.neurobiolaging.2019.09.008.
Bassett, D. S. and Bullmore, E. T., “Small-world brain networks revisited,” Neuroscientist, 23, No, 5, 499–516 (2017), https://doi.org/10.1177/1073858416667720.
Bassett, D. S. and Sporns, O., “Network neuroscience,” Nat. Neurosci., 20, No, 3, 353–364 (2017).
Bassett, D. S., Meyer-Lindenberg, A., Achard, S., et al., “Adaptive reconfiguration of fractal small-world human brain functional networks,” Proc. Natl. Acad. Sci. USA, 103, No. 51, 19518–19523 (2006), https://doi.org/10.1073/pnas.0606005103.
Bernhardt, B. C., Bonilha, L., and Gross, D. W., “Network analysis for a network disorder: the emerging role of graph theory in the study of epilepsy,” Epilepsy Behav., 50, 162–170 (2015), https://doi.org/10.1016/j.yebeh.2015.06.005.
Boersma, M., Smit, D. J. A., Boomsma, D. I., et al., “Growing trees in child brains: graph theoretical analysis of electroencephalography-derived minimum spanning tree in 5-and 7-year-old children reflects brain maturation,” Brain Connect., 3, No. 1, 50–60 (2013), https://doi.org/10.1089/brain.2012.0106.
Boersma, M., Smit, D. J. A., de Bie, H. M. A., et al., “Network analysis of resting state EEG in the developing young brain: structure comes with maturation,” Hum. Brain Mapp., 32, No, 3, 413–425 (2011), https://doi.org/10.1002/hbm.21030.
Boldyreva, G. N., Sharova, E. V., and Dobronravova, I. S., “The role of regulatory structures in the foration of the human EEG,” Fiziol. Cheloveka, 26, No, 5, 19–34 (2000).
Boldyreva, G. N., Zhavoronkova, L. A., Sharova, E. V., and Dobronravova, I. S., “Electroencephalographic intercentral interaction as a reflection of normal and pathological human brain activity,” Span. J. Psychol., 10, No, 1, 169–179 (2007), https://doi.org/10.1017/s1138741600006430.
Bordier, C., Nicolini, C., and Bifone, A., “Graph analysis and modularity of brain functional connectivity networks: searching for the optimal threshold,” Front. Neurosci., 11, 1–9 (2017), https://doi.org/10.3389/fnins.2017.0041.
Bornholdt, S. and Schuster, H. G. (eds.), Handbook of Graphs and Networks: from the Genome to the Internet, Wiley-VCH, Weinheim (2003), https://doi.org/10.1002/3527602755.
Bosch-Bayard, J., Girini, K., Biscay, R. J., et al., “Resting EEG effective connectivity at the sources in developmental dysphonetic dyslexia. Differences with non-specific reading delay,” Int. J. Psychophysiol., 153, 135–147 (2020), https://doi.org/10.1016/j.ijpsycho.2020.04.021.
Buchanan, C. R., Bastin, M. E., Ritchie, S. J., et al., “The effect of network thresholding and weighting on structural brain networks in the UK Biobank,” NeuroImage, 211, 1–14 (2020), https://doi.org/10.1016/j.neuroimage.2019.116443.
Buckner, R. L., Sepulcre, J., Talukdar, T., et al., “Cortical hubs revealed by intrinsic functional connectivity: Mapping, assessment of stability, and relation to Alzheimer’s disease,” J. Neurosci., 29, No, 6, 1860–1873 (2009), https://doi.org/10.1523/jneurosci.5062-08.2009.
Bullmore, E. and Sporns, O., “Complex brain networks: graph theoretical analysis of structural and functional systems,” Nat. Rev. Neurosci., 10, No, 3, 186–198 (2009), https://doi.org/10.1038/nrn2575.
Bullmore, E. and Sporns, O., “The economy of brain network organization,” Nat. Rev. Neurosci., 13, No, 5, 336–349 (2012), https://doi.org/10.1038/nrn3214.
Cacciola, A., Naro, A., Milardi, D., et al., “Functional brain network topology discriminates between patients with minimally conscious state and unresponsive wakefulness syndrome,” Int. J. Clin. Med., 8, No. 3, 1–22 (2019), https://doi.org/10.3390/jcm8030306.
Cao, R., Hao, Y., Wang, X., et al., “EEG functional connectivity underlying emotional valance and arousal using minimum spanning trees,” Front. Neurosci., 14, 1–12 (2020), https://doi.org/10.3389/FNINS.2020.00355/BIBTEX.
Cao, Z., Lin, C. T., Chuang, C. H., et al., “Resting-state EEG power and coherence vary between migraine phases,” J. Headache Pain, 17, No, 1, 1–9 (2016), https://doi.org/10.1186/s10194-016-0697-7.
Carrasco-Gómez, M., Keijzer, H. M., Ruijter, B. J., et al., “EEG functional connectivity contributes to outcome prediction of postanoxic coma,” Clin. Neurophysiol., 132, 1312–1320 (2021), https://doi.org/10.1016/j.clinph.2021.02.011.
Chen, Y., Huang, X., Wu, M., et al., “Disrupted brain functional networks in drug-naive children with attention deficit hyperactivity disorder assessed using graph theory analysis,” Hum. Brain Mapp., 40, No, 17, 4877–4887 (2019), https://doi.org/10.1002/hbm.24743.
Chen, Z. J., He, Y., Rosa-Neto, P., et al., “Revealing modular architecture of human brain structural networks by using cortical thickness from MRI,” Cereb. Cortex, 18, No, 10, 2374–2381 (2008), https://doi.org/10.1093/cercor/bhn003.
Chennu, S., Annen, J., Wannez, S., et al., “Brain networks predict metabolism, diagnosis and prognosis at the bedside in disorders of consciousness,” Brain, 140, No. 8, 2120–2132 (2017), https://doi.org/10.1093/brain/awx163.
Chennu, S., Finoia, P., Kamau, E., et al., “Spectral signatures of reorganised brain networks in disorders of consciousness,” PLoS Comput. Biol., 10, No, 10, 1–16 (2014), https://doi.org/10.1371/journal.pcbi.1003887.
Chernii, V. I., Andronova, I. A., Gorodnik, G. A., et al., “Studies of EEG predictors for neurotransmitter and neuroglial activity and the features of rearrangements in intercenter relationships in the brain in patients with severe TBI,” Mezhdunarod. Nevrol. Zh., 5, No. 83, 41–54 (2016), https://doi.org/10.22141/2224-0713.5.83.2016.78470.
Collin, G. and van den Heuvel, M. P., “The o ntogeny of the human connectome: development and dynamic changes of brain connectivity across the life span,” Neuroscientist, 19, No, 6, 616–628 (2013), https://doi.org/10.1177/1073858413503712.
Crobe, A., Demuru, M., Didaci, L., et al., “Minimum spanning tree and k-core decomposition as measure of subject-specific EEG traits,” Biomed. Phys. Eng. Express, 2, No. 1, 1–16 (2016), https://doi.org/10.1088/2057-1976/2/1/017001.
Dai, Z., de Souza, J., Lim, J., et al., “EEG cortical connectivity analysis of working memory reveals topological reorganization in theta and alpha bands,” Front. Hum. Neurosci., 11, 1–13 (2017), https://doi.org/10.3389/fnhum.2017.00237.
Dai, Z., Lin, Q., Li, T., et al., “Disrupted structural and functional brain networks in Alzheimer’s disease,” Neurobiol. Aging, 75, 71–82 (2019), https://doi.org/10.1016/j.neurobiolaging.2018.11.005.
Dehaene, S., Changeux, J.-P., and Naccache, L., “The global neuronal workspace model of conscious access: From neuronal architectures to clinical applications,” in: Characterizing Consciousness: From Cognition to the Clinic? Research and Perspectives in Neurosciences, Dehaene, S., and Christen, Y. (eds.), Springer, Berlin, Heidelberg (2011), Vol. 18, pp. 55–84, https://doi.org/10.1007/978-3-642-18015-6_4.
Dehaene, S., Changeux, J.-P., Naccache, L., et al., “Conscious, preconscious, and subliminal processing: a testable taxonomy,” Trends Cogn. Sci., 10, No, 5, 204–211 (2006), https://doi.org/10.1016/j.tics.2006.03.007.
Dell’Italia, J., Johnson, M. A., Vespa, P. M., and Monti, M. M., “Network analysis in disorders of consciousness: four problems and one proposed solution (exponential random graph models),” Front. Neurol., 9, 439–459 (2018).
Demertzi, A., Tagliazucchi, E., Dehaene, S., et al., “Human consciousness is supported by dynamic complex patterns of brain signal coordination,” Sci. Adv., 5, No. 2, 1–11 (2019), https://doi.org/10.1126/sciadv.aat7603.
Dickie, D. A., Shenkin, S. D., Anblagan, D., et al., “Whole brain magnetic resonance image atlases: A systematic review of existing atlases and caveats for use in population imaging,” Front. Neuroinform., 11, 1–15 (2017), https://doi.org/10.3389/fninf.2017.00001.
Douw, L., Schoonheim, M. M., Landi, D., et al., “Cognition is related to resting-state small-world network topology: an magnetoencephalographic study,” Neuroscience, 175, 169–177 (2011), https://doi.org/10.1016/j.neuroscience.2010.11.039.
Douw, L., van Dellen, E., Gouw, A. A., et al., “The road ahead in clinical network neuroscience,” Netw. Neurosci., 3, No. 4, 969–993 (2019), https://doi.org/10.1162/netn_a_00103.
Egorov, Yu. V. and Kuznetsova, G. D., The Brain as a Volume Conductor, Institute of Higher Nervous Activity and Neurophysiology, Nauka, Moscow (1976).
Faber, J., Antoneli, P. C., Via, G., et al., “Critical elements for connectivity analysis of brain networks,” in: Functional Brain Mapping: Methods and Aims, Tsytsarev, V. et al. (eds.) (2020), pp. 67–107, https://doi.org/10.1007/978-981-15-6883-1_4.
Fagiolo, G., “Clustering in complex directed networks,” Phys. Rev. E, 76, No, 2, 1–16 (2007).
Farahani, F. V., Karwowski, W., and Lighthall, N. R., “Application of graph theory for identifying connectivity patterns in human brain networks: a systematic review,” Front. Neurosci., 13, 1–27 (2019), https://doi.org/10.3389/fnins.2019.00585.
Farashi, S. and Khosrowabadi, R., “EEG based emotion recognition using minimum spanning tree,” Phys. Eng. Sci. Med., 43, No, 3, 985–996 (2020), https://doi.org/10.1007/s13246-020-00895-y.
Feklicheva, I. V., Chipeeva, N. A., Zakharov, I. M., et al., “The interaction of intelligence and resting-state functional connectivity in the brain,” Teor. Eksperim. Psikhol., 13, No, 30, 65–80 (2020).
Finotelli, P., Forlim, C. G., Klock, L., et al., “New graph-theoretical-multimodal approach using temporal and structural correlations reveals disruption in the thalamo-cortical network in patients with schizophrenia,” Brain Connect., 9, No. 10, 760–769 (2019), https://doi.org/10.1089/brain.2018.0654.
Fornito, A. and Bullmore, E. T., “Connectomics: a new paradigm for understanding brain disease,” Eur. Neuropsychopharmacol., 25, No, 5, 733–748 (2015), https://doi.org/10.1016/j.euroneuro.2014.02.011.
Fox, P. T. and Friston, K. J., “Distributed processing: distributed functions?” NeuroImage, 61, No, 2, 407–426 (2012), https://doi.org/10.1016/j.neuroimage.2011.12.051.
Franciotti, R., Falasca, N. W., Arnaldi, D., et al., “Cortical network topology in prodromal and mild dementia due to Alzheimer’s disease: graph theory applied to resting state EEG,” Brain Topogr., 32, No, 1, 127–141 (2019), https://doi.org/10.1007/s10548-018-0674-3.
Fries, P., “Rhythms for cognition: Communication through coherence,” Neuron, 88, No, 1, 220–235 (2015), https://doi.org/10.1016/j.neuron.2015.09.034.
Friston, K. J., “Functional and effective connectivity in neuroimaging: a synthesis,” Hum. Brain Mapp., 2, No. 1–2, 56–78 (1994).
Friston, K. J., “The free-energy principle: a rough guide to the brain?” Trends Cogn. Sci., 13, No, 7, 293–301 (2009), https://doi.org/10.1016/j.tics.2009.04.005.
Friston, K. J., Frith, C. D., Liddle, P. F., and Frackowiak, R. S., “Functional connectivity: the principal- component analysis of large (PET) data sets,” J. Cereb. Blood Flow Metab., 13, No, 1, 5–14 (1993), https://doi.org/10.1038/jcbfm.1993.4.
Girn, M., Mills, C., and Christoff, K., “Linking brain network reconfiguration and intelligence: Are we there yet?” Trends Neurosci. Educ. 15, 62–70 (2019), https://doi.org/10.1016/j.tine.2019.04.001.
Gnezditskii, V. V., The Inverse EEG Problem and Clinical Electroencephalography, Medpressinform, Moscow (2004).
Gong, G., He, Y., Concha, L., et al., “Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography,” Cereb. Cortex, 19, No, 3, 524–536 (2009), https://doi.org/10.1093/cercor/bhn102.
Grindel’, O. M. and Sazonova, O. B., “Introduction to clinical EEG,” in: Neurophysiological Clinical Investigations, Antidor, Moscow (2001), pp. 13–16.
Grindel’, O. M., “The optimum EEG coherence level in assessments of the functional state of the human brain,” Zh. Vyssh. Nerv. Deyat., 30, No. 1, 62–70 (1980).
Gutman, A. M., The Biophysics of Extracellular Currents in the Brain, Nauka, Moscow (1980).
Guye, M., Bettus, G., Bartolomei, F., and Cozzone, P. J., “Graph theoretical analysis of structural and functional connectivity MRI in normal and pathological brain networks,” MAGMA, 23, No, 5, 409–421 (2010), https://doi.org/10.1007/s10334-010-0205-z.
Habas, C. (ed.), The Neuroimaging of Brain Diseases, Springer Int. Publ. (2018), https://doi.org/10.1007/978-3-319-78926-2.
Hagmann, P., Cammoun, L., Gigandet, X., et al., “Mapping the structural core of human cerebral cortex,” PLoS Biol., 6, No. 7, 1479–1493 (2008), https://doi.org/10.1371/journal.pbio.0060159.
Hagmann, P., Kurant, M., Gigandet, X., et al., “Mapping human wholebrain structural networks with diffusion MRI,” PLoS One, 2, No. 7, 1–9 (2007), https://doi.org/10.1371/journal.pone.0000597.
Hamzeh, M., Vahidi, B., and Nematollahi, A. F., “Optimizing configuration of cyber network considering graph theory structure and teaching learning-based optimization (GT-TLBO),” IEEE Trans. Industr. Inform., 15, No, 4, 2083–2090 (2019), https://doi.org/10.1109/TII.2018.2860984.
Harary, F., Graph Theory [Russian translation], Mir, Moscow (1973).
Hasan, M. A. H., Khan, M. U., and Mishra, D. A., “Computationally efficient method for hybrid EEG-fNIRS BCI based on the Pearson correlation,” BioMed Res. Int., 2020, 1–13 (2020), https://doi.org/10.1155/2020/1838140.
Hassan, M., Dufor, O., Merlet, I., et al., “EEG source connectivity analysis: from dense array recordings to brain networks,” PLoS One, 9, No. 8, 1–15 (2014), https://doi.org/10.1371/journal.pone.0105041.
Hatlestad-Hall, C., Bruña, R., Syvertsen, M. R., et al., “Source-level EEG and graph theory reveal widespread functional network alterations in focal epilepsy,” Clin. Neurophysiol., 132, No. 7, 1663–1676 (2021).
He, Y., Chen, Z. J., and Evans, A. C., “Small-world anatomical networks in the human brain revealed by cortical thickness from MRI,” Cereb. Cortex, 17, No, 10, 2407–2419 (2007), https://doi.org/10.1093/cercor/bhl149.
Hilgetag, C. C. and Kaiser, M., “Clustered organization of cortical connectivity,” Neuroinformatics, 2, No. 2, 353–360 (2004), https://doi.org/10.1385/NI:2:3:353.
Hilgetag, C. C., Beul, S. F., van Albada, S. J., and Goulas, A., “An architectonic type principle integrates macroscopic cortico-cortical connections with intrinsic cortical circuits of the primate brain,” Netw. Neurosci., 3, No. 4, 905–923 (2019), https://doi.org/10.1162/netn_a_00100.
Humphries, M. D. and Gurney, K., “Network ‘small-world-ness’: a quantitative method for determining canonical network equivalence,” PLoS One, 3, No. 4, 1–10 (2008), https://doi.org/10.1371/journal.pone.0002051.
Ioannou, P., Computational Modelling of Working Memory: PhD Thesis, University of Surrey, UK (2014), pp. 1–104.
Ion, A., Kropatsch, W. G., and Haxhimusa, Y., “Considerations regarding the minimum spanning tree pyramid segmentation method,” in: Proc. 11th Workshop on Structural, Syntactic, and Statistical Pattern Recognition (SSPR), LNCS (2006), Vol. 4109, pp. 182–190.
Iturria-Medina, Y., Sotero, R. C., Canales-Rodriguez, E. J., et al., “Studying the human brain anatomical network via diffusion-weighted MRI and graph theory,” NeuroImage, 40, No, 3, 1064–1076 (2008).
Ivanov, L. B., Applied Computerized Electroencephalography, MBN, Moscow (2004).
Iznak, A. F., Iznak, E. V., and Mel’nikova, T. S., “EEG coherence parameters as a reflection of brain neuroplasticity in mental pathology (literature review),” Psikhiatriya, 78, No, 2, 127–137 (2018), https://doi.org/10.30629/2618-6667-2018-78-127-137.
Jatoi, M. A. and Kamel, N., Brain Source Localization Using EEG Signal Analysis, CRC Press (2017).
Kennedy, H., Van Essen, D. C., and Christen, Y., Micro-, Meso- and Macro- Connectomics of the Brain, Springer Nature (2016).
Khramov, A. E., Frolov, N. S., Maksimenko, V. A., et al., “Functional networks of the brain: from restoration of connections to dynamic integration,” Usp. Fiz. Nauk., 191, No. 6, 614–650 (2021), https://doi.org/10.3367/UFNr.2020.06.038807.
Knyazev, G. G., Volf, N. V., and Belousova, L. V., “Age-related differences in electroencephalogram connectivity and network topology,” Neurobiol. Aging, 36, No, 5, 1849–1859 (2015).
Koessler, L., Maillard, L., Benhadid, A., et al., “Automated cortical projection of EEG sensors: anatomical correlation via the international 10–10 system,” NeuroImage, 46, No, 1, 64–72 (2009).
Kunszenti-Kovács, D., Lovász, L., and Szegedy, B., “Measures on the square as sparse graph limits,” J. Comb. Theory. Ser. B, 138, 1–40 (2019).
Larsen, J. C., “Electrical network theory of countable graphs,” IEEE Trans. Circuits Syst. I. Regul. Pap., 44, No, 11, 1045–1055 (1997).
Latora, V. and Marchiori, M., “Efficient behavior of small-world networks,” Phys. Rev. Lett., 87, 1–4 (2001), https://doi.org/10.1103/PhysRevLett.87.198701.
Liao, X., Vasilakos, A. V., and He, Y., “Small-world human brain networks: perspectives and challenges,” Neurosci. Biobehav. Rev., 77, 286–300 (2017), https://doi.org/10.1016/j.neubiorev.2017.03.018.
Liégeois, R., Santos, A., Matta, V., et al., “Revisiting correlation-based functional connectivity and its relationship with structural connectivity,” Netw. Neurosci., 4, No. 4, 1235–1251 (2020).
Liégeois, R., Ziegler, E., Geurts, P., et al., “Cerebral functional connectivity periodically (de) synchronizes with anatomical constraints,” Brain Struct. Funct., 221, No. 6, 2985–2997 (2014), https://doi.org/10.1007/s00429-015-1083-y.
Lin, P., Sun, J., Yu, G., et al., “Global and local brain network reorganization in attention-deficit/hyperactivity disorder,” Brain Imaging Behav., 8, No. 4, 558–569 (2014), https://doi.org/10.1007/s11682-013-9279-3.
Lisacheva, P. D., Mel’nikov, M. E., and Shtark, M. B., “Genetic aspects of fMRI studies of the brain,” Usp. Fiziol. Nauk., 51, No, 1, 58–71 (2020), https://doi.org/10.31857/S0301179820010075.
Livanov, M. N., Spatal Organization of Processes in the Brain, Nauka, Moscow (1972).
Lopes da Silva, F., EEG: Origin and Measurement. EEG-fMRI, Physiological Basis, Technique and Applications, Mulert, C. and Lemieux, L. (eds.), Springer Verlag, Berlin-Heidelberg (2010).
Lord, L. D., Stevner, A. B., Deco, G., and Kringelbach, M. L., “Understanding principles of integration and segregation using whole-brain computational connectomics: implications for neuropsychiatric disorders,” Phil. Trans. Roy. Soc. Lond. A Phys. Eng. Sci., 375, 1–21 (2017), https://doi.org/10.1098/rsta.2016.0283.
Machinskaya, R. I., Rozovskaya, R. I., Kurganskii, A. V., and Pechenkova, E. V., “Cortical functional inteaections while holding emotionally colored images in working memory. Analysis of EEG theta-rhythm cohernece in the space of sources,” Fiziol. Cheloveka, 42, No, 3, 56–73 (2016), https://doi.org/10.7868/S0131164616020120.
Maksimenko, V. A., Runnova, A. E., Frolov, N. S., et al., “Multiscale neural connectivity during human sensory processing in the brain,” Phys. Rev. E, 97, 1–10 (2018), https://doi.org/10.1103/PhysRevE.97.052405.
Mannil, M. and Winklhofer, S. F.-X. (eds.), Neuroimaging Techniques in Clinical Practice, Springer Nature Switzerland AG (2020), https://doi.org/10.1007/978-3-030-48419-4.
Martynova, O. V., Sushinskaya-Tetereva, A. O., Balaev, V. V., and Ivanitskii, A. M., “Correlations of functional connections of brain areas active in the resting state with behavioral and psychological indicators,” Zh. Vyssh. Nerv. Deyat., 66, No, 5, 541–555 (2016), https://doi.org/10.7868/S0044467716050063.
McColgan, P., Blom, T., Rees, G., et al., “Stability and sensitivity of structural connectomes: effect of thresholding and filtering and demonstration in neurodegeneration,” bioRxiv Preprint https://doi.org/10.1101/416826.
Meier, J., Tewarie, P., Hillebrand, A., et al., “Mapping between structural and functional brain networks,” Brain Connect., 6, No. 4, 298–311 (2016), https://doi.org/10.1089/brain.2015.0408.
Merinov, A. A. and Kochkarov, A. A., “Analysis of the network structure of the connectome of the human brain and its classification,” Sovremen. Nauka, 3, 9–16 (2016).
Michel, C. M. and Brunet, D., “EEG source imaging: a practical review of the analysis steps,” Front. Neurol., 10, 1–18 (2019), https://doi.org/10.3389/fneur.2019.00325.
Micheloyannis, S., “Graph-based network analysis in schizophrenia,” World J. Psychiatry, 2, No. 1, 1–12 (2012), https://doi.org/10.5498/wjp.v2.i1.1.
Micheloyannis, S., Pachou, E., Stam, C. J., et al., “Small-world networks and disturbed functional connectivity in schizophrenia,” Schizophr. Res., 87, No, 1–3, 60–66 (2006).
Miraglia, F., Vecchio, F., Bramanti, P., and Rossini, P. M., “EEG characteristics in “eyes-open” versus “eyes-closed” conditions: small-world network architecture in healthy aging and age-related brain degeneration,” Clin. Neurophysiol., 127, No. 2, 1261–1268 (2016).
Newman, M. E. J., “Modularity and community structure in networks,” Proc. Natl. Acad. Sci. USA, 103, No. 23, 8577–8696 (2006), https://doi.org/10.1073/pnas.0601602103.
Newman, M. E. J., “The structure and function of complex networks,” SIAM Rev., 45, No, 2, 167–256 (2003).
Nunez, P. L. and Srinivazan, R., “Electric fields of the brain,” in: The Neurophysics of EEG, Oxford University Press (1981).
Olejarczyk, E. and Jernajczyk, W., “Graph-based analysis of brain connectivity in schizophrenia,” PLoS One, 12, No, 11, 1–28 (2017), https://doi.org/10.1371/journal.pone.0188629.
Onnela, J. P., Saramäki, J., Kertész, J., and Kaski, K., “Intensity and coherence of motifs in weighted complex networks,” Phys. Rev. E, 71, No, 6, 1–5 (2005), https://doi.org/10.1103/physreve.71.065103.
Pascual-Marqui, R. D., Biscay, R. J., Bosch-Bayard, J., et al., “Assessing direct paths of intracortical causal information flow of oscillatory activity with the isolated effective coherence (iCoh),” Front. Hum. Neurosci., 8, No. 448, 1–12 (2014), https://doi.org/10.3389/fnhum.2014.00448.
Pascual-Marqui, R. D., Esslen, M., Kochi, K., and Lehmann, D., “Functional imaging with low-resolution brain electromagnetic tomography (LORETA, a review,” Methods Find. Exp. Clin. Pharmacol., 24, 91–95 (2002).
Pascual-Marqui, R. D., Lehmann, D., Koukkou, M., et al., “Assessing interactions in the brain with exact low-resolution electromagnetic tomography,” Philos. Trans. R. Soc. A, 369, No. 1952, 3768–3784 (2011).
Peraza, L. R., Asghar, A. U., Green, G., and Halliday, D. M., “Volume conduction effects in brain network inference from electroencephalographic recordings using phase lag index,” J. Neurosci. Meth., 207, No. 2, 189–199 (2012), https://doi.org/10.1016/j.jneumeth.2012.04.007.
Pfurtscheller, G., Schwerdtfeger, A. R., Seither-Preisler A, et al., “Brainheart communication: Evidence for “central pacemaker” oscillations with a dominant frequency at 0.1 Hz in the cingulum,” Clin. Neurophysiol., 128, No. 1, 183–193 (2017), https://doi.org/10.1016/j.clinph.2016.10.097.
Phillips, D. J., McGlaughlina, A., Rutha, D., et al., “Graph theoretic analysis of structural connectivity across the spectrum of Alzheimer’s disease: The importance of graph creation methods,” NeuroImage Clin., 2015, No. 7, 377–390 (2015), https://doi.org/10.1016/j.nicl.2015.01.007.
Ponomarev, V. A., Cryptic Electroencephalogram Sources and Event-Related Potentials and their Significance: Dissertation, Pavlov Institute of Physiology (2016).
Pospelov, N., Nechaev, S., Anokhin, K., et al., “Spectral peculiarity and criticality of a human connectome,” Phys. Life Rev., 31, 240–256 (2021).
Požar, R., Giordani, B., and Kavcic, V., “Effective differentiation of mild cognitive impairment by functional brain graph analysis and computerized testing,” PLoS One, 15, No, 3, 1–19 (2020), https://doi.org/10.1371/journal.pone.0230099.
Proshina, E. A., Savostyanov, A. N., Bocharov, A. V., and Knyazev, G. G., “Effect of 5-HTTLPR on current source density, connectivity, and topological properties of resting state EEG networks,” Brain Res., 1697, 67–75 (2018), https://doi.org/10.1016/j.brainres.2018.06.018.
Rubinov, M. and Sporns, O., “Complex network measures of brain connectivity: uses and interpretations,” NeuroImage, 52, No, 3, 1059–1069 (2010).
Rubinov, M., Ypma, R. J., Watson, C., and Bullmore, E. T., “Wiring cost and topological participation of the mouse brain connectome,” Proc. Natl. Acad. Sci. USA, 112, No. 32, 10032–10037 (2015), https://doi.org/10.1073/pnas.1420315112.
Rusinov, V. S., Grindel’, O. M., Boldyreva, G. N., and Vakar, E. M., Biopotentials of the Human Brain, Meditsina, Moscow (1987).
Rusinov, V. S., The Dominant, USSR Academy of Medical Sciences, Meditsina, Moscow (1969).
Saramäki, J., Kivelä, M., Onnela, J. P., et al., “Generalizations of the clustering coefficient to weighted complex networks,” Phys. Rev. E Stat. Nonlin. Biol. Soft Matter Phys., 75, No, 2, 1–4 (2007), https://doi.org/10.1103/PhysRevE.75.027105.
Schoffelen, J. M. and Gross, J., “Source connectivity analysis with MEG and EEG,” Hum. Brain Mapp., 30, 1857–1865 (2009), https://doi.org/10.1002/hbm.20745.
Sharaev, M. G., Zavyalova, V. V., Ushakov, V. L., et al., “Effective connectivity within the default mode network: Dynamic causal modeling of resting-state fMRI data,” Front. Hum. Neurosci., 10, 1–9 (2016), https://doi.org/10.3389/fnhum.2016.00014.
Sharova, E. V., “Asymmetry of EEG coherence in post-coma unconscious states after severe traumatic brain injury,” in: Functional Interhemisphere Asymmetry after Severe Traumatic Brain Injury. A Reader, Bogolepova, N. N. and Fokina, V. F. (eds.), Nauchnyi Mir, Moscow (2004), pp. 578–585.
Sharova, E. V., “Current potentials of the EEG in the analysis of functional impairments in severe brain injuries,” Neironauk. Teor. Klin. Asp. (Ukr.), 5, No. 1–2, 49–58 (2009).
Sharova, E. V., Pogosbekyan, E. L., Korobkova, E. V., et al., “Interhemispheric connectivity and attention in patients with disorders of consciousness after severe traumatic brain injury,” J. Neurol.,” Stroke, 8, No. 4, 245–253 (2018), https://doi.org/10.15406/jnsk.2018.08.00319.
Shepoval’nikov, A. N., Tsitseroshin, M. N., and Pogosyan, A. A., “The role of different areas of the cortex and their connections in forming spatially ordered brain biopotentials fields in postnatal ontogeny,” Fiziol. Cheloveka, 23, No, 2, 12–24 (1997).
Shine, J. M., Breakspear, M., Bell, P. T., et al., “Human cognition involves the dynamic integration of neural activity and neuromodulatory systems,” Nat. Neurosci., 22, No, 2, 289–296 (2019), https://doi.org/10.1038/s41593-018-0312-0.
Simard, D., Nadeau, L., and Kröger, H., “Fastest learning in small-world neural networks,” Phys. Lett. A, 336, No. 1, 8–15 (2005).
Singer, W., “Distributed processing and temporal codes in neuronal networks,” Cogn. Neurodyn., 3, No. 3, 189–196 (2009).
Sporns, O. and Zwi, J. D., “The small world of the cerebral cortex,” Neuroinformatics, 2, No. 2, 145–162 (2004).
Sporns, O., “Graph theory methods: applications in brain networks,” Dialogues Clin. Neurosci., 20, No, 2, 111–121 (2018).
Sporns, O., Honey, C. J., and Kötter, R., “Identification and classification of hubs in brain networks,” PLoS One, 2, No. 10, 10–49 (2007).
Sporns, O., Networks of the Brain, MIT Press, Cambridge, MA (2010).
Steriade, M., Gloor, P., Llinás, R. R., et al., “Basic mechanisms of cerebral rhythmic activities,” Electroencephalogr. Clin. Neurophysiol., 76, No, 6, 481–508 (1990).
Stumme, J., Jockwitz, C., Hoffstaedter, F., et al., “Functional network reorganization in older adults: Graph-theoretical analyses of age, cognition and sex,” NeuroImage, 214, 1–15 (2020), https://doi.org/10.1016/j.neuroimage.2020.116756.
Suárez, L. E., Markello, R. D., Betzel, R. F., and Misic, B., “Linking structure and function in macroscale brain networks,” Trends Cogn. Sci., 24, No, 4, 302–315 (2020), https://doi.org/10.1016/j.tics.2020.01.008.
Sviderskaya, N. E., Spatial Organization of the Electroencephalogram, VGMA Press, Moscow (2008).
Szalkai, B., Kerepesi, C., Varga, B., and Grolmusz, V., “Parameterizable consensus connectomes from the human connectome project: The Budapest reference connectome server v3/0,” Cogn. Neurodyn., 11, No, 1, 113–116 (2017), https://doi.org/10.1007/s11571-016-9407-z.
Tan, B., Kong, X., Yang, P., et al., “The difference of brain functional connectivity between eyes-closed and eyes-open using graph theoretical analysis,” Comput. Math. Methods Med., 2013, 1–15 (2013), https://doi.org/10.1155/2013/976365.
Termenon, M., Jaillard, A., Delon-Martin, C., and Achard, S., “Reliability of graph analysis of resting state fMRI using test-retest dataset from the Human Connectome Project,” NeuroImage, 142, 172–187 (2016), https://doi.org/10.1016/j.neuroimage.2016.05.062.
Tononi, G., Sporns, O., and Edelman, G. M., “A measure for brain complexity: relating functional segregation and integration in the nervous system,” Proc. Natl. Acad. Sci. USA, 91, No, 11, 5033–5037 (1994).
Tóth, B., Urbán, G., Háden, G. P., et al., “Large-scale network organization of EEG functional connectivity in newborn infants,” Hum. Brain Mapp., 38, No, 8, 4019–4033 (2017), https://doi.org/10.1002/hbm.23645.
Ushakov, V. L. and Velichkovskii, B. M., “Visualization of large-scale networks in the brain,” Nauka Innovats., 12, No, 154, 22–25 (2015).
Ustimenko, V., “On computations with Double Schubert Automaton and stable maps of Multivariate Cryptography,” arXiv preprint (2021), https://doi.org/10.48550/arXiv.2108.08288.
Vaessen, M. J., Hofman, P. A., Tijssen, H. N., et al., “The effect and reproducibility of different clinical DTI gradient sets on small world brain con-nectivity measures,” NeuroImage, 51, No, 3, 1106–1116 (2010).
Van den Heuvel, M. P. and Hulshoff Pol, H. E., “Exploring the brain network: A review on resting-state fMRI functional connectivity,” Eur. Neuropsychopharmacol., 20, 519–534 (2010), https://doi.org/10.1016/j.euroneuro.2010.03.008.
Van den Heuvel, M. P. and Sporns, O., “A cross-disorder connectome landscape of brain dysconnectivity,” Nat. Rev. Neurosci., 20, No, 7, 435–446 (2019).
Van den Heuvel, M. P. and Sporns, O., “An anatomical substrate for integration among functional networks in human cortex,” J. Neurosci., 33, No, 36, 14489–14500 (2013), https://doi.org/10.1523/jneurosci.2128-13.2013.
Vecchio, F., Gorgoni, M., Ferrara, M., et al., “Cortical connectivity modulation during sleep onset: A study via graph theory on EEG data,” Hum. Brain Mapp., 38, No, 11, 5456–5464 (2017a), https://doi.org/10.1002/hbm.23736.
Vecchio, F., Miraglia, F., and Rossini, M. P., “Connectome: Graph theory application in functional brain network architecture,” Clin. Neurophysiol. Pract., 24, No, 2, 206–213 (2017b), https://doi.org/10.1016/j.cnp.2017.09.003.
Vecchio, F., Miraglia, F., and Rossini, P. M., “Connectome: Graph theory application in functional brain network architecture,” Clin. Neurophysiol., 2, 206–213 (2017c), https://doi.org/10.1016/j.cnp.2017.09.003.
Viola, E. and Wigderson, A., “Local expanders,” Comput. Complex., 27, No, 2, 225–244 (2018).
Wang, J., Zuo, X., and He, Y., “Graph-based network analysis of resting- state functional MRI,” Front. Syst. Neurosci., 4, No. 16, (2010), https://doi.org/10.3389/fnsys.2010.00016.
Watanabe, H. and Shinoda, S., “Soul of circuit theory. A review on research activities of graphs and circuits in Japan,” IEEE Trans. Circuits Systems I: Fund. Theory Appl., 46, No, 1, 83–94 (1999).
Watts, D. J. and Strogatz, S. H., “Collective dynamics of ‘small-world’ networks,” Nature, 393, No. 6684, 440–442 (1998).
Wendelken, C., Ferrer, E., Ghetti, S., et al., “Frontoparietal structural connectivity in childhood predicts development of functional connectivity and reasoning ability: A large-scale longitudinal investigation,” J. Neurosci., 37, No, 35, 8549–8558 (2017), https://doi.org/10.1523/JNEUROSCI.3726-16.2017.
Wu, G., Munsell, B., Laurienti, P., and Chung, M. K., “GRAND: Unbiased Connectome Atlas of Brain Network by Groupwise Graph Shrinkage and Network Diffusion,” in: Connectomics in NeuroImaging, Wu, G. et al. (eds.), Lecture Notes in Computer Science, CNI 2018, Springer, Cham (2018), Vol. 11083, pp. 127–135, https://doi.org/10.1007/978-3-030-00755-3_14.
Xia, M., Wang, J., and He, Y., “BrainNet Viewer: a network visualization tool for human brain connectomics,” PLoS One, 8, No. 7, 1–15 (2013), https://doi.org/10.1371/journal.pone.0068910.
Zeng, K., Kang, J., Ouyang, G., et al., “Disrupted brain network in children with autism spectrum disorder,” Sci. Rep., 7, No. 1, 1–12 (2017), https://doi.org/10.1038/s41598-017-16440-z.
Zhavoronkova, L. A., Interhemisphere Asymmetry of the Human Brain (right-handers, left-handers), Yurait, Moscow (2019), 3rd ed.
Zhu, G., Li, Y., and Wen, P. P., “Analysis and classification of sleep stages based on difference visibility graphs from a single-channel EEG signal,” IEEE J. Biomed. Health Inform., 18, No, 6, 1813–1821 (2014), https://doi.org/10.1109/JBHI.2014.2303991.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zhurnal Vysshei Nervnoi Deyatel’nosti imeni I. P. Pavlova, Vol. 72, No. 6, pp. 741–767, November–December, 2022.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Vigasina, K.D., Proshina, E.A., Gotovtsev, P.M. et al. Approaches to the Use of Graph Theory to Study the Human EEG in Health and Cerebral Pathology. Neurosci Behav Physi 53, 381–398 (2023). https://doi.org/10.1007/s11055-023-01437-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11055-023-01437-1