Neo4j support multiple relationships (edges) between two nodes of the graph.
If you are using Cypher for working with Graph here is Query for your example:
CREATE (su:SuperUser { name:'Super User'}) //Create Node with Label SuperUser and property Name with value 'Super User'
CREATE (dc:DataClassification { name:'Data Classification C'}) //Create Node with Label DataClassification and property Name with value 'Data Classification C'
CREATE (su)-[:READ]->(dc) //Create relationship with Label READ
CREATE (su)-[:CREATEUPDATE]->(dc) //Create relationship with Label CREATEUPDATE
CREATE (su)-[:DELETE]->(dc) //Create relationship with Label DELETE