brain-higher-order-structures

To analyze higher-order interactions in fMRI brain networks, construct simplicial complexes from functional connectivity matrices. This approach captures multi-node interactions across scales that traditional pairwise analyses miss.

Betti numbers and persistent homology reveal the topological features of brain networks by quantifying higher-order structures. Computing these metrics generates persistence summaries to characterize topological changes in health and disease.

Yes, you can use both resting-state and task-driven fMRI correlation matrices to build simplicial complexes. The methodology applies to functional connectivity data to assess multi-node interactions across scales.

You need numpy, scipy, gudhi, ripser, and networkx to compute persistent homology for brain network analysis. These Python libraries handle numerical and topological analysis to compute Betti numbers and generate persistence summaries.

The best way to quantify higher-order structures beyond pairwise functional connectivity is using simplicial complexes. This topological approach identifies and quantifies multi-node interactions that traditional pairwise network analyses miss.