The vibrational dynamics of a new class of cross-linked polymers made up of cyclodextrins is here investigated in the microscopic range by the joint use of light and inelastic neutron scattering experiments. The effect of increasing the connectivity of the polymeric network on the vibrational dynamics of the system is studied by exploiting the complementarity of these two different probes. The derived densities of vibrational states of the polymers evidence the presence of the characteristic anomalous excess of vibrational modes with respect to the Debye level, already observed in the low-frequency Raman spectra and referred to as boson peak (BP). The overall analysis of the spectra suggests an emerging picture in which the motions of hydrogen atoms of the polymers are progressively hampered when the cross-linking degree of the covalent network increases. At the same time, the frequency and intensity of the BP are found to significantly change by increasing the cross-linking degree of the polymeric network, as clearly suggested by the existence of a scaling-law for the BP evolution. These findings support the conclusion that the growing of the covalent connectivity of the system induces a general modifications of the elastic properties of these cyclodextrin-based polymers, which are, once again, modulated by the cross-linking agent/cyclodextrin molar ratio.