  Deep interferometric observations of CO and dust continuum emission are
obtained with the Sub-Millimeter Array (SMA) at 230 GHz to investigate the
physical nature of the giant molecular cloud (GMC) population in the Andromeda
galaxy (M31). We use J = 2-1 $^{12}$CO and $^{13}$CO emission to derive the
masses, sizes and velocity dispersions of 162 spatially resolved GMCs. We
perform a detailed study of a subset of 117 GMCs that exhibit simple, single
component line profile shapes. Examining the Larson scaling relations for these
GMCs we find: 1- a highly correlated mass-size relation in both $^{12}$CO and
$^{13}$CO emission; 2- a weakly correlated $^{12}$CO linewidth-size (LWS)
relation along with a weaker, almost non-existent, $^{13}$CO LWS relation,
suggesting a possible dependence of the LWS relation on spatial scale; and
3-that only 43\% of these GMCs are gravitationally bound. We identify two
classes of GMCs based on the strength and extent of their $^{13}$CO emission.
Examination of the Larson relations finds that both classes are individually
characterized by strong $^{12}$CO mass-size relations and much weaker $^{12}$CO
and $^{13}$CO LWS relations. The majority (73\%) of strong $^{13}$CO emitting
GMCs are found to be gravitationally bound. However, only 25\% of the weak
$^{13}$CO emitting GMCs are bound. The resulting breakdown in the Larson
relations in the weak $^{13}$CO emitting population decouples the mass-size and
LWS relations demonstrating that independent physical causes are required to
understand the origin of each. Finally, in nearly every aspect, the physical
properties of the M31 GMCs are found to be very similar to those of local Milky
Way clouds.
