  We study ideal Bose gas upon two scale-free structures with identical degree
distribution. Energy spectra belonging to tight-binding Hamiltonian are exactly
solved and the related spectral dimensions of $G_1$ and $ G_2$ are obtained as
$d_{s_1} = 2$ and $d_{s_2} = 2 \ln 4/ \ln 3$. We show Bose-Einstein
condensation will only take place upon $G_2$ instead of $G_1$. The topology and
thermodynamical property of the two structures are proven to be totally
different.
