Chemical cycling drives the production and loss of many important atmospheric constituents. The speed of atmospheric chemical cycling is a particularly valuable indicator for characterizing and measuring the effects of such cycles on oxidant chemistry, air quality, and climate. Here, we apply graph theoretical methods to explicitly quantify and analyze the characteristic timescales of chemical cycles in the atmosphere, as simulated by the GEOS-Chem chemical mechanism. We identify all two-, three-, and four-reaction cycles in the mechanism and calculate a characteristic timescale for each individual cycle. We find that the speed of chemical cycling varies by orders of magnitude at any given location but tends to be faster in urban- and biogenically-dominated chemical regions, and slower during the night. We further quantify the fraction of cycling that contains a rate-determining step, and explicitly demonstrate the large potential for mechanisms to recycle oxidants like OH.