The importance of the whole: topological data analysis for the network neuroscientist

Understand

The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems.

• Among many important contributions, networks have proven useful in identifying sets of node pairs that are densely connected and that collectively support brain function.
• Yet the restriction to pairwise interactions prevents us from realizing intrinsic topological features such as cavities within the interconnection structure that may be just as crucial for proper function.
• To detect and quantify these topological features we must turn to methods from algebraic topology that encode data as a simplicial complex built of sets of interacting nodes called simplices.