With the rise of large neuroimaging datasets, scientists now work with detailed maps of brain connectivity—network representations that show how hundreds of brain regions fluctuate and coordinate their activity over time. But making sense of these enormous networks poses a challenge: What patterns matter? Which changes signal healthy aging, and which reflect differences associated with autism spectrum disorder (ASD)?

The study introduces a mathematical innovation that helps answer precisely these questions. Researchers applied persistent homology, a tool from topological data analysis (TDA), to detect how brain connectivity reorganizes during healthy aging and in ASD.