A method for operating a graph processing system including a first and second memory, comprising: storing in the first memory, a start index, a terminal index and an edge value of graph data; storing in the second memory, a start vertex of the graph data; rearranging the start vertex as an intermediate vertex by using to the start index; performing a graph computation on the intermediate vertex by using to the terminal index and the edge value; storing in the second memory, a terminal vertex as a result of the graph computation; determining whether a graph processing operation is completed by comparing the terminal vertex and the start vertex; setting the terminal vertex as the start vertex when the graph processing operation is not completed; and iterating the rearranging, the performing, the storing the terminal vertex, the determining and the setting until the graph processing operation is completed.