In this paper we examine how Discretionary Access Control principles, that have been successfully applied to relational and XML data, can be applied to the Resource Description Framework (RDF) graph data model. The objective being to provide a baseline for the specification of a general authorisation framework for the RDF data model. Towards this end we provide a summary of access control requirements for graph data structures, based on the different characteristics of graph models compared to relational and tree data models. We subsequently focus on the RDF data model and identify a list of access rights based on SPARQL query operations; propose a layered approach to authorisation derivation based on the graph structure and RDFSchema; and demonstrate how SQL GRANT and REVOKE commands can be adapted to cater for delegation of privileges in SPARQL.