Tutorial on brain network and topological data analysis. Code snips available here: https://pub.towardsai.net/computing-and-visualizing-brain-topological-data-analysis-511635158ae2 A connectome is a graph/network representation of the brain, where one node is a brain region, and edges are either representation of structural connections or strength of correlation of brain activity. We talk about structural connectome in the first case and functional connectome in the latter. This kind of representation has been used by thousands of researchers to extract biomarkers or to study intrinsic aspects of the brain. It allows the identification of local network differences or the use of metrics that summarize important aspects of the networks as segregation and integration. However, to capture high-order interactions between regions (nodes) we need to move from pairwise network metrics to simplicial complexes. Simplicial complex A simplicial complex is a set composed of points, line segments, triangles, and their n-dimensional counterparts. 0-simplex is a vertex, 1-simplex is an edge connecting 2 nodes, 2-simplex is a triangle, and so on. Persistent homology Persistent homology is a technique for computing the topological properties of space (in the discreet case of a network) at various spatial resolutions. In order to determine whether there were homology classes that “persisted” through several filtrations, persistent homology records the appearance of cycles across the evolving simplicial complexes during filtration. #brain #neuroscience #network