  A statistical measure of dimension is used to compute the effective average
space dimension for the Internet and other graphs, based on typed edges (links)
from an ensemble of starting points. The method is applied to CAIDA's ITDK data
for the Internet. The effective dimension at different scales is calibrated to
the conventional Euclidean dimension using low dimensional hypercubes. Internet
spacetime has a 'foamy' multi-scale containment hierarchy, with interleaving
semantic types. There is an emergent scale for approximate long range order in
the device node spectrum, but this is not evident at the AS level, where there
is finite distance containment. Statistical dimension is thus a locally varying
measure, which is scale-dependent, giving an visual analogy for the hidden
scale-dependent dimensions of Kaluza-Klein theories. The characteristic
exterior dimensions of the Internet lie between 1.66 +- 0.00 and 6.12 +- 0.00,
and maximal interior dimensions rise to 7.7.
