The solar minimum at the transition from cycle 23 to 24 was notable for its low level of activity and its extended duration. Among the various fields of study, the evolution of the solar convection zone may provide insight into the causes and consequences of this recent minimum. This study continues previous investigations of the characteristics of solar supergranulation, a convection component strongly linked to the structure of the magnetic field, namely the time-evolution of the global mean of supergranule cell size, determined from spectral analysis of MDI Dopplergrams from the two previous solar minima. Analyses of the global mean of supergranule sizes show a quasi-oscillatory nature to the evolution of this particular supergranule characteristic. Performing similar analyses on realistic, synthetic Doppler images show similar time-dependent characteristics. We conclude that the observed fluctuations are not observational artifacts, and that an underlying trend exists within the evolution of the supergranulation network.