Figure 1

Schematic outlining point cloud to persistence diagram. (left) A point set (representing atomic centers) with balls of increasing radius around the points, (right) 1-dimensional persistence diagram of the point set. Representative cycles, corresponding to the points in the diagram, are highlighted with matching colors. The larger the loop, the higher the persistence value (\(death-birth\)). Figure created with Ipe 7.2.23 (http://ipe.otfried.org/).