Finding a Maximum Common Subgraph from Molecular Structural Formulas through the Maximum Clique Approach Combined with the Ising Model

We examined the maximum common subgraph (MCS) of four neuraminidase inhibitors that were antiviral medication for treating and preventing type A and B influenza viruses. The MCS was obtained by finding a maximum clique of an association graph constructed from the two input chemical structural formulas. Maximum clique problem was reformulated to Ising Hamiltonian to allow for applying various techniques for optimization. We observed that the combined label for a vertex composed of elemental species and chemical bonds significantly worked well for decreasing the number of vertices in the association graph, which in turn helped to reduce the computational cost.