  Diffusion on a diluted hypercube has been proposed as a model for glassy
relaxation and is an example of the more general class of stochastic processes
on graphs. In this article we determine numerically through large scale
simulations the eigenvalue spectra for this stochastic process and calculate
explicitly the time evolution for the autocorrelation function and for the
return probability, all at criticality, with hypercube dimensions $N$ up to
N=28. We show that at long times both relaxation functions can be described by
stretched exponentials with exponent 1/3 and a characteristic relaxation time
which grows exponentially with dimension $N$. The numerical eigenvalue spectra
are consistent with analytic predictions for a generic sparse network model.
