Connectomics, graph theory and functional MRI

The brain is an extraordinarily complex network. It thus stands to reason that methods for modelling the structure and dynamics of networks should be useful for understanding the brain. Graph theory, a branch of mathematics concerned with systems of interacting elements, provides a natural formalism for modelling complex networks, including the brain, and rests on the assumption that all such networks can be represented as a graph of nodes connected by edges. The nodes represent fundamental processing units or elements of the network; for example, in nervous systems, nodes could represent individual neurons or large-scale brain regions. The edges represent some kind of interaction between elements; for example, some measure of structural or functional brain connectivity. Once the nodes and edges are defined, graph theory offers a rich repertoire of diverse measures for quantifying different aspects of network organization and function. In this talk, I will introduce and motivate the use of graph theory for the analysis of functional MRI and discuss critical issues associated with building a valid graph theoretic model of the brain, with a focus on methods for defining nodes and edges. I will then consider practical issues associated with analysing brain graphs, focusing on the analysis of both network connectivity and topology, and provide example applications at each step.

Acknowledgements

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References

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