This article provides a new solution to problems about graph clustering by DNA computing

and also provides some new ideas on seeking for minimum cuts in the DNA two-stage method and afterwards future analyses a graph.Before carrying out the DNA two-stage method

some formation should be made on the given diagram to make it suitable for the premise of DNA two-stage method.Then when implementing the two-stage method

we shall encode the vertex and edge in the given graph first.After some biochemical reactions

it can generate all the routes from the source node to the sink node about the formatted graph.Then we could figure out the minimum cut of the given source node and the sink node through some computing

thus complete the division of the graph.Finally we can implement the two-stage methods iteratively until the satisfying cluster number is found.Besides

this article offers the testimony of the algorithm as well

which further illustrates its feasibility.