  There is proposed a model of scale-free random graphs which are locally close
to the uncorrelated complex random networks with divergent $\langle k^2
\rangle$ studied in e.g. S. N. Dorogovtsev {\it et al}, Rev. Mod. Phys. {\bf
80}, 1275 (2008). It is shown that the Ising model on these graphs with
interaction intensities of arbitrary signs with probability one is in a
paramagnetic state at sufficiently high finite values of the temperature. For
the same graphs, the bond percolation model with probability one is in a
nonpercolative state for positive values of the percolation probability.
Possible extensions are discussed.
