1. A transitive closure system comprising: a database comprising a cached transitive closure; at least one processor; and a transitive closure management module embodied on non-transitory computer readable medium including instructions translatable by the at least one processor to perform: receiving an identification of an entity defined in the database; interacting with a relational database management system receiving queries according to a relational query language, said interacting incrementally updating the cached transitive closure comprising: generating a new transitive closure for the entity from a directed graph; determining a delete transitive closure record, said determining the delete transitive closure record comprising: comparing the new transitive closure and cached transitive closure to determine a first transitive closure path for the entity that is not specified in the new transitive closure and that is specified in the cached transitive closure; and selecting a cached transitive closure record identifying the first transitive closure path as the delete transitive closure record; and deleting the delete transitive closure record from the cached transitive disclosure.