Fig. 1: Graphical representation of the evolution of the persistent diagram (PD) for anisole.

a Each atom of anisole is represented by a point. Each connected component is born at time birth = 0 in the evolution of b homological features plot and c PD. Each bar at the evolution plot tracks the connected components or holes. Note that there are 16 overlapping points in the PD associated with the number of atoms. d–f The radius of a sphere centered at each atom is increased, and the connected components continue to persist so the persistence of a connected component is not in its final location. g–i When the radius increase leads to sphere overlap between atom pairs, the connected components on the PD are finalized. A hole is created by the six carbon atoms of the phenyl group, and a blue triangle appears in the persistence diagram to indicate its birth. j–l The radius is again expanded, and the hole (phenyl ring) still persists. m–o A second hole is formed between the methoxyl group and the two carbons of the phenyl group. The death of both holes occurs when their corresponding spheres intersect. The final PD is obtained when the death of all but one connected component and all holes are observed. Note that the bottom bar never terminates and it is always excluded from the PD.