Recently, another cloud taxonomy service in addition to IaaS, PaaS and Saas services has been added: this is the business process as a service in the cloud (BPaaS). A BPaaS is any business process delivered through a cloud service model via internet with access through web interfaces. Therefore, process models will be developed by providers for discovery and use by tenants. In a previous work, we perform the design of an e-learning process as a business process in cloud. This paper examines the problem of discovering the similarity between e-learning processes. Given a pair of e-learning process models, the consumer lunches a request and the provider present a target process. The query is thus compared to the target process in order to check if it answers to the user needs. To achieve this goal, we use the graph based structural matching process and apply the graph edit edit-distance to measure the similarity between the two processes. We demonstrate the feasibility of our approach by testing the greedy and A-Star algorithms. The results we obtained show the efficiency and precision of the A-Star algorithm compared to the greedy algorithm.