Network theory-based approaches provide valuable insights into the variations in global structural connectivity between differing dynamical states of proteins. Our objective is to review network-based analyses to elucidate such variations, especially in the context of subtle conformational changes. We present technical details of the construction and analyses of protein structure networks, encompassing both the non-covalent connectivity and dynamics. We examine the selection of optimal criteria for connectivity based on the physical concept of percolation. We highlight the advantages of using side-chain based network metrics in contrast to backbone measurements. As an illustrative example, we apply the described network approach to investigate the global conformational change between the closed and partially open states of the SARS-CoV-2 spike protein. This conformational change in the spike protein is crucial for coronavirus entry and fusion into human cells. Our analysis reveals global structural reorientations between the two states of the spike protein despite small changes between the two states at the backbone level. We also observe some differences at strategic locations in the structures, correlating with their functions, asserting the advantages of the side-chain network analysis. Finally we present a view of allostery as a subtle synergistic-global change between the ligand and the receptor, the incorporation of which would enhance the drug design strategies.