Recently, there has been a lot of research on graph-type data because it can model seamless the application domains such as GIS, network, WWW, multimedia presentations etc., and domain in which the data sequence is important. In this paper, an efficient code system, called node code system, is proposed to evaluate paths of DAG in a multimedia presentation graph. The node code system assigns a unique binary string to each node of a graph. The comparison of node codes of two nodes tells the connectivity between the nodes without actual traversal of a graph. The method using the property of the node code system allows us to construct the paths between two nodes more efficiently than the method using conventional graph traversals. The algorithms to construct paths using the node code system are provided.