Graph Theory and Neural Networks
Graph theory has been applied to neuroscience to increase our understanding of the complex interactions within neural networks in very exciting ways. “Graph theory is a branch of mathematics that deals with the formal description and analysis of graphs. A graph is defined simply as a set of nodes (vertices) linked by connections (edges), and may be directed or undirected. When describing a real-world system, a graph provides an abstract representation of the system’s elements and their interactions” (Bullmore and Sporns, 2009, p. 186).
ONLINE LECTURE
Brown - Graph theory (Fri Jul 13 2012 02:05:08 PM)
This is a lecture by Jesse Brown for the UCLA NeuroImaging Training Program in 2012. The NeuroImaging Training Program at UCLA is part of an NIH-sponsored training grant. Their mission is to promote deep knowledge of neuroimaging methods, rigorous analysis approach and cutting edge image processing and analysis.
ABSTRACT
Complex brain networks: graph theoretical analysis of structural and functional systems
Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain’s structural and functional systems have features of complex networks — such as small-world topology, highly connected hubs and modularity — both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field. [Bullmore & Sporns (2009). Nature Reviews Neuroscience, 10: 186-198.]
FURTHER READING
ONLINE LECTURE
Brown - Graph theory (Fri Jul 13 2012 02:05:08 PM)
This is a lecture by Jesse Brown for the UCLA NeuroImaging Training Program in 2012. The NeuroImaging Training Program at UCLA is part of an NIH-sponsored training grant. Their mission is to promote deep knowledge of neuroimaging methods, rigorous analysis approach and cutting edge image processing and analysis.
ABSTRACT
Complex brain networks: graph theoretical analysis of structural and functional systems
Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain’s structural and functional systems have features of complex networks — such as small-world topology, highly connected hubs and modularity — both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field. [Bullmore & Sporns (2009). Nature Reviews Neuroscience, 10: 186-198.]
FURTHER READING
- Assessment of system dysfunction in the brain through MRI-based connectomics [Filippi et al. (2013) Lancet Neurol Epib ahead of print.]
- Abnormalities of functional brain networks in pathological gambling: a graph-theoretical approach. [Tschernegg, et al. (2013) Front Hum Neurosci, 7:625.]
- Aberrant topographical organization in gray matter structural network in late life depression: a graph theoretical analysis. [Lim, et al. (2013) Int Psychogeriatr, Oct 7:1-12, EPub ahead of print.]
- Test-retest reliability of fMRI-based graph theoretical properties during working memory, emotion processing, and resting state. [Cao, et al. (2013) Neuroimage, Sep 18, EPub ahead of print.]
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