has been developed as a more accurate and efficient method for biomolecular graph analysis [@KLXia:2013d; @Opron:2014]. In particular, aided with a cell lists algorithm [@Allen:1987], the fast FRI (fFRI) is about ten percent more accurate than GNM on a test set of 364 proteins and is orders of magnitude faster than GNM on a set of 44 proteins, due to its ${\cal O}(N)$ computational complexity. It has been demonstrated that fFRI is able to predict the B-factors of an entire HIV virus capsid with 313,236 residues in less than 30 seconds on a single-core processor, which would require GNM more than 120 years to accomplish if its computer memory were not a problem [@Opron:2014].

Topological analysis of molecules has become very popular since the introduction of the theory of atoms in molecules (AIM) for molecular electron density data by Bader and coworkers [@Bader:1985; @Bader:1990]. AIM was proposed to quantitatively define the atomic bonds and interatomic surfaces (IASs) by employing a topology based partition of electron density. It has two main strands: the scalar field topology of molecular electron density maps and the scalar field topology of the local Laplacian of electron density [@Popelier:2000; @Popelier:2005]. The former characterizes chemical bonds and 