Incremental graph processing has been developed to reduce unnecessary redundant calculations in dynamic graphs. In this paper, we propose an incremental dynamic graph-processing scheme using a cost model to selectively perform incremental processing or static processing. The cost model calculates the predicted values of the detection cost and processing cost of the recalculation region based on the past processing history. If there is a benefit of the cost model, incremental query processing is performed. Otherwise, static query processing is performed because the detection cost and processing cost increase due to the graph change. The proposed incremental scheme reduces the amount of computation by processing only the changed region through incremental processing. Further, it reduces the detection and disk I/O costs of the vertex, which are calculated by reusing the subgraphs from the previous results. The processing structure of the proposed scheme stores the data read from the cache and the adjacent vertices and then performs only memory mapping when processing these graph. It is demonstrated through various performance evaluations that the proposed scheme outperforms the existing schemes.