An Algebra Approach for Finding Frequent Subgraphs with Hamiltonian Cycle

When referred to functional motif discovery in biological network and drug target recognition in pharmaceutical chemistry, the most important step is to mine subgraphs with certain structure in a graph. Fortunately we notice that those kinds of subgraphs are frequently characterized by a Hamiltonian cycle. Hence, in this paper we develop a matrix theory based approach for mining such subgraphs. Firstly we study the properties of Hamiltonian subgraphs and determine the k-path based on the properties to find subgraph with Hamiltonian cycle. Then, an algorithm for mining subgraph with Hamiltonian cycle is designed under the frame of this approach. Finally, we analyze the complexity of the algorithm and simulate it on five real networks to verify our algorithms. The simulation results show that our algorithms have high efficiency.