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There is proposed a model of scale-free random graphs which are locally closeto the uncorrelated complex random networks with divergent $\langle k^2\rangle$ studied in e.g. S. N. Dorogovtsev {\it et al}, Rev. Mod. Phys. {\bf80}, 1275 (2008). It is shown that the Ising model on these graphs withinteraction intensities of arbitrary signs with probability one is in aparamagnetic state at sufficiently high finite values of the temperature. Forthe same graphs, the bond percolation model with probability one is in anonpercolative state for positive values of the percolation probability.Possible extensions are discussed.

On thermodynamic states of the Ising model on scale-free graphs