Encyclopedia of Clinical Neuropsychology

2018 Edition
| Editors: Jeffrey S. Kreutzer, John DeLuca, Bruce Caplan

Graph Theory

  • Brock KirwanEmail author
  • Ty Bodily
Reference work entry
DOI: https://doi.org/10.1007/978-3-319-57111-9_9069

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. 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. 2.

    Estimation of the connectivity probability or coherence between...

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References and Readings

  1. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  2. 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.CrossRefGoogle Scholar
  3. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  4. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. 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.CrossRefGoogle Scholar
  7. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  8. 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.PubMedCrossRefPubMedCentralGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Psychology Department and the Neuroscience CenterBrigham Young UniversityProvoUSA