While criticism has been levelled at persistence diagrams for how much they rely on qualitative analysis (see refs. ; Ormrod ; ), if that is what's desired they can be extremely useful. The analysis of persistence diagrams is simplified if instead we track whether particular features in a network persistent across time instead of length scale. The medium-range order as represented by a ring structure in a network is especially interesting to us, as it is often hardest to track. In this analysis, we define a ring R as being constructed of a unique set of moleculesfor example, a square might be made up of molecules {1, 2, 3, 4} and a second triangle could be made up of molecules {4, 5, 6, 7}. We then can calculate an existence function f (t; R) for each ring R over time t during a trajectory of interest. This function f (t; R) has a major difference from the usual filtration functions used for persistent homology in that a single ring can be born, die, and live again. For example, the square {4, 5, 6, 7} could exist at t = 1, die at t = 2, be reborn at t = 3 and die a final time at t = 4 as seen in the right bar of Figure . This leads to the persistence diagram in Figure striped in both directions, which will be useful for analysis of repair phenomena. The lifespan of a given ring can be defined as L(R) = ∞ 0 f (t; R)dt, and birthdeath diagrams can be plotted using the first birth and final death of a given ring.