Centrality dependence of forward-backward (FB) multiplicity correlations in Au–Au collisions in the energy range, \(\sqrt{s} = \) 14.5 to 200 GeV (RHIC) and Pb–Pb collisions at \(\sqrt{s_{NN}} = \) 2.76 to 5.02 TeV (LHC) are studied with HYDJET++ model and the findings are compared with those reported for the ALICE data. It is observed that FB multiplicity correlations from the soft thermal component include nearly equal contributions from short-range correlations caused by the resonance decays and long-range correlations arising due to hydrodynamical particle flow. The increasing strength of correlation with beam energy is due to growing contributions from the hard-jets, particularly in the central collisions. However, for predicting correct dependence of correlation strength on the collision centrality, contributions from both soft and hard components should be taken into account simultaneously.