  We conduct numerical simulations of a model of four dimensional quantum
gravity in which the path integral over continuum Euclidean metrics is
approximated by a sum over combinatorial triangulations. At fixed volume the
model contains a discrete Einstein-Hilbert term with coupling $\kappa$ and
local measure term with coupling $\beta$ that weights triangulations according
to the number of simplices sharing each vertex. We map out the phase diagram in
this two dimensional parameter space and compute a variety of observables that
yield information on the nature of any continuum limit. Our results are
consistent with a line of first order phase transitions with a latent heat that
decreases as $\kappa\to\infty$. We find a Hausdorff dimension along the
critical line that approaches $D_H=4$ for large $\kappa$ and a spectral
dimension that is consistent with $D_s=\frac{3}{2}$ at short distances. These
results are broadly in agreement with earlier works on Euclidean dynamical
triangulation models which utilize degenerate triangulations and/or different
measure terms and indicate that such models exhibit a degree of universality.
