collection. Therefore, only the B-factors for specific types of atoms, say C$_\alpha$ atoms, can be directly interpreted as their relative flexibility without corrections. Another important method for accessing protein flexibility is nuclear magnetic resonance (NMR) which often provides structural flexibility information under physiological conditions. NMR spectroscopy allows the characterization of protein flexibility in diverse spatial dimensions and a large range of time scales. About six percent of structures in the PDB are determined by electron microscopy (EM) which does not directly offer the flexibility information at present. Therefore, it is important to have mathematical or biophysical methods to predict their flexibility.

Graph theory related methodologies {#sec:graph}
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With the development of experimental tools, vast amount of data for biomolecular structures and interaction networks are available and provide us with unprecedented opportunities in mathematical modeling. The graph theory and network models have been widely used in the study of biomolecular structures and interactions and found many applications in drug design, protein function analysis, gene identification, RNA structure representation, etc. [@DasGupta2016; @Gan:2004rag; @Fera:2004rag] Generally speaking, biomolecular graph and network models can be divided into two major categories, namely, abstract graph/network models, which include biomolecular interaction-network models, and geometric graph/network models, where the 