The folded structures of proteins can be accurately predicted by deep learning algorithms from their amino-acid sequences. By contrast, in spite of decades of research studies, the prediction of folding pathways and the unfolded and misfolded states of proteins, which are intimately related to diseases, remains challenging. A two-state (folded/unfolded) description of protein folding dynamics hides the complexity of the unfolded and misfolded microstates. Here, researchers focus on the development of simplified order parameters to decipher the complexity of disordered protein structures. First, researchers show that any connected, undirected, and simple graph can be associated with a linear chain of atoms in thermal equilibrium. This analogy provides an interpretation of the usual topological descriptors of a graph, namely the Kirchhoff index and Randic resistance, in terms of effective force constants of a linear chain. The Kirchhoff index is the inverse of a global force constant K of the graph. Researchers derive an exact relation between this global force constant and the average shortest path length (l) of the graph. Second, researchers represent the three-dimensional protein structures by connected, undirected, and simple graphs. As a proof of concept, researchers compute the topological descriptors K and l for an all-atom molecular dynamics trajectory of folding/unfolding events of the proteins Trp-cage and HP-36 and for the ensemble of experimental NMR models of Trp-cage. The video shows the fluctuations of K and l as a function of time and the associated dynamical protein graph. The present video shows that the local, nonlocal, and global force constants and free energies of a protein graph are promising tools to quantify unfolded/disordered protein states and folding/unfolding dynamics. In particular, they allow the detection of transient misfolded rigid states.