Use case diagram is one of the behaviour diagrams in UML diagrams. It models the basic needs of users and how users and systems interact to achieve them. Each use case diagram forms a structure which abides a set of standard notations and grammar. Therefore, we can measure the structural similarity between the two use case diagrams. Measuring the similarity of two use case diagram structures can help in the process of reusing diagrams, detecting clones, and assessing learning results. This study proposes an advanced method to measure the structural similarity between the two use case diagrams. Each use case diagram is translated into a graph. The graph represents the inter-structure and intra-structure of a diagram. The graph inter-structure models the interaction between the main use cases and their actors. In comparison, the graph intra-structure models the detailed structure descriptions of every main use case. The similarity between the two represented graph calculates using Greedy Graph Edit Distance. Our experimental result shows that the proposed graph can measure the similarity of the use case structural diagram. The Greedy Graph Edit Distance also can calculate the similarity other UML diagrams for the specific purpose.