Tailoring physical and chemical properties at the nanoscale by assembling nanoparticles currently paves the way for new functional materials. Obtaining the desired macroscopic properties is usually determined by a perfect control of the contact between nanoparticles. Therefore, the physics and chemistry of nanocontacts are one of the central issues for the design of the nanocomposites. Since the birth of atomic force microscopy, crucial advances have been achieved in the quantitative evaluation of van der Waals and Casimir forces in nanostructures and of adhesion between the nanoparticles. We present here an investigation, by a noncontact method, of the elasticity of an assembly of nanoparticles interacting via either van der Waals-bonded or covalent-bonded coating layers. We demonstrate indeed that the ultrafast opto-acoustic technique, based on the generation and detection of hypersound by femtosecond laser pulses, is very sensitive to probe the properties of the nanocontacts. In particular, we observe and evaluate how much the subnanometric molecules present at nanocontacts influence the coherent acoustic phonon propagation along the network of the interconnected silica nanoparticles. Finally, we show that this ultrafast opto-acoustic technique provides quantitative estimates of the rigidity/stiffness of the nanocontacts.