Techniques described herein allow a user of an RDBMS to specify a graph algorithm function (GAF) declaration, which defines a graph algorithm that takes a graph object as input and returns a logical graph object as output. A database dictionary stores the GAF declaration, which allows addition of GAFs without changing the RDBMS kernel. GAFs are used within graph queries to compute output properties of property graph objects. Output properties are accessible in the enclosing graph pattern matching query, and are live for the duration of the query cursor execution. According to various embodiments, the declaration of a GAF includes a DESCRIBE function, used for semantic analysis of the GAF, and an EXECUTE function, which defines the operations performed by the GAF. Furthermore, composition of GAFs in a graph query is done by supplying, as the input graph argument of an outer GAF, the result of an inner GAF.