The success of nanoparticle-based devices will need reliable fabrication methods for well-defined, defect-free self-assembled structures of nanoparticles (NPs). NP self-assembly is a process governed by an interplay between many inter-particle interactions, such as core-core van der Waals and dipolar attractions, as well as interactions of the ligand shells, which, when generating an interpenetration, is called interdigitation. The result of this delicate balance between strong interactions is often kinetically hindered; hence, the reaching and recognition of an equilibrium structure becomes challenging. Here, a systematic study is presented that aims at approaching equilibrium 2D NP assemblies (i.e., NP monolayers) based on cyclic compression and relaxation in Langmuir NP monolayers. Cyclic isotherm curves are taken at various surface pressures together with a complete characterization of the corresponding structural evolution of the NP structures. Results are obtained through the analysis of the images, using in-house software that enables the analysis and visualization of the degree of ligand interdigitation as well as the NPs short-and long-range order. It is found that the initial structures obtained through Langmuir assembly can be quite far from equilibrium, mostly due to inhomogeneities in the ligand shell interdigitation and interaction. A few compression cycles render the whole assembly more homogeneous and significantly increases the long-range order. Finally, this structural analysis shows that the ligand shell can act a buffer to the size polydispersity in the particle cores.