Exactly solvable tight-binding models on two scale-free networks with   identical degree distribution
  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. 
Pinchen Xie, Zhongzhi Zhang, Bo Wu
cond-mat.quant-gas cond-mat.stat-mech