Research grants have played an important role in seeding and promoting fundamental research projects worldwide. There is a growing demand for developing and delivering scientific influence analysis as a service on research grant repositories. Such analysis can provide insight on how research grants help foster new research collaborations, encourage cross-organizational collaborations, influence new research trends, and identify technical leadership. This paper presents the design and development of a grants-based scientific influence analysis service, coined as GImpact. It takes a graph-theoretic approach to design and develop large scale scientific influence analysis over a large research-grant repository with three original contributions. First, we mine the grant database to identify and extract important features for grants influence analysis and represent such features using graph theoretic models. For example, we extract an institution graph and multiple associated aspect-based collaboration graphs, including a discipline graph and a keyword graph. Second, we introduce self-influence and co-influence algorithms to compute two types of collaboration relationship scores based on the number of grants and the types of grants for institutions. We compute the self-influence scores to reflect the grant based research collaborations among institutions and compute multiple co-influence scores to model the various types of cross-institution collaboration relationships in terms of disciplines and subject areas. Third, we compute the overall scientific influence score for every pair of institutions by introducing a weighted sum of the self-influence score and the multiple co-influence scores and conduct an influence-based clustering analysis. We evaluate GImpact using a real grant database, consisting of 2512 institutions and their grants received over a period of 14 years...