Synonyms
Association matrix; Brain Connectivity Toolbox; Complex network analysis; Connectivity probability; Diffusion tensor imaging; DTI; EEG; Electrode; Electroencephalogram; fMRI; Functional magnetic resonance imaging; Graph theory; Magnetoencephalography; MEG; Network analysis; Neuroimaging; Nodes; Pair-wise data; Probability; Small-worldness; Voxels; Whole-brain network
Definition
Graph theory is a mathematically driven approach to understanding complex networks. It consists of the application of analytical approaches to network data in graph form. Building such a network graph requires four steps (Bullmore and Sporns 2009):
- 1.
The definition of a set of nodes, each of which corresponds to an anatomically defined brain region from histological, fMRI, or DTI data. The nodes could also be individual neurons or a measurement source, such as an fMRI voxel, EEG electrode, or an electrode in a multielectrode array.
- 2.
Estimation of the connectivity probability or coherence between each...
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences and Readings
Achard, S., Salvador, R., Whitcher, B., Suckling, J., & Bullmore, E. (2006). A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. Journal of Neuroscience, 26(1), 63–72. https://doi.org/10.1523/JNEUROSCI.3874-05.2006.
Bernhardt, B. C., Bonilha, L., & Gross, D. W. (2015). Network analysis for a network disorder: The emerging role of graph theory in the study of epilepsy. Epilepsy & Behavior, 50, 162–170. https://doi.org/10.1016/j.yebeh.2015.06.005.
Bullmore, E., & Sporns, O. (2009). Complex brain networks: Graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience, 10(3), 186–198. https://doi.org/10.1038/nrn2575.
van den Heuvel, M. P., & Fornito, A. (2014). Brain networks in schizophrenia. Neuropsychology Review, 24(1), 32–48. https://doi.org/10.1007/s11065-014-9248-7.
Reijneveld, J. C., Ponten, S. C., Berendse, H. W., & Stam, C. J. (2007). The application of graph theoretical analysis to complex networks in the brain. Clinical Neurophysiology, 118(11), 2317–2331. https://doi.org/10.1016/j.clinph.2007.08.010.
Rubinov, M., & Sporns, O. (2010). Complex network measures of brain connectivity: Uses and interpretations. NeuroImage, 52(3), 1059–1069. https://doi.org/10.1016/j.neuroimage.2009.10.003.
Stam, C. J., & Reijneveld, J. C. (2007). Graph theoretical analysis of complex networks in the brain. Nonlinear Biomedical Physics, 1(1), 3. https://doi.org/10.1186/1753-4631-1-3.
Tijms, B. M., Wink, A. M., de Haan, W., van der Flier, W. M., Stam, C. J., Scheltens, P., et al. (2013). Alzheimer’s disease: Connecting findings from graph theoretical studies of brain networks. Neurobiology of Aging, 34(8), 2023–2036. https://doi.org/10.1016/j.neurobiolaging.2013.02.020.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this entry
Cite this entry
Kirwan, B., Bodily, T. (2018). Graph Theory. In: Kreutzer, J.S., DeLuca, J., Caplan, B. (eds) Encyclopedia of Clinical Neuropsychology. Springer, Cham. https://doi.org/10.1007/978-3-319-57111-9_9069
Download citation
DOI: https://doi.org/10.1007/978-3-319-57111-9_9069
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-57110-2
Online ISBN: 978-3-319-57111-9
eBook Packages: Behavioral Science and PsychologyReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences