distance geometry plays an important role.

The geometric graph models or biomolecular structure graph models construct unique graphs based on biomolecular 3D structural data. The graph theory is then employed to analyze biomolecular properties in four major aspects: flexibility and rigidity analysis, protein mode analysis, protein domain decomposition and biomolecular nonlinear dynamics. Many other network based approaches, including GNM [@Bahar:1997; @Bahar:1998] and ANM [@Atilgan:2001], have been developed for protein flexibility analysis. More recently, FRI has been proposed as a matrix-decomposition-free method for flexibility analysis, [@KLXia:2013d; @Opron:2014]. The fundamental assumptions of the FRI method are as follows. Protein functions, such as flexibility, rigidity, and energy, are fully determined by the structure of the protein and its environment, and the protein structure is in turn determined by the relevant interactions. Therefore, whenever a native protein structure is available, there is no need to analyze protein flexibility and rigidity by tracing back to the protein interaction Hamiltonian. Consequently, the FRI bypasses the ${\cal O}(N^3)$ matrix diagonalization. In fact, FRI does not even require the 3D geometric information of the protein structure. It assesses graphic connectivity of the protein distance geometry and analyzes the geometric compactness of the protein structure. It can be regarded 