as a kernel generalization of the local density model [@Halle:2002; @DWLi:2009; @CPLin:2008]. Another very important application of biomolecular structure graph model is the protein mode analysis. As stated above, the low order eigenmodes provide information of the protein dynamics at equilibrium state. Normal mode analysis (NMA) plays important roles in mode analysis. However, its potential function involves too many interactions and it is very inefficient for large biomolecular systems. Anisotropic network model (ANM) has dramatically reduced the complexity of the potential function by representing the biological macromolecule as an elastic mass-and-spring network. In the network each node is a C$_\alpha$ atom of the associated residue and springs represent the interactions between the nodes. The overall potential is the sum of harmonic potentials between interacting nodes. To describe the internal motions of the spring connecting two atoms, there is only one degree of freedom. Qualitatively, this corresponds to the compression and expansion of the spring in a direction given by the locations of the two atoms. In other words, ANM is an extension of the GNM to three coordinates per atom, thus accounting for directionality.

The biomolecular structure graph models can also be used in protein domain decomposition. The biomolecular structural 