The disclosed embodiments provide a system for processing queries of a graph database. During operation, the system stores intermediate results of the query in a structure comprising rows in a set of tables and links between pairs of rows in different tables in the set of tables. Next, the system tracks, in the structure, representations of data, relationships, and path consistency in the query. The system then applies one or more operations to existing rows in the structure to generate a final result of the query. Finally, the system provides the final result in a response to the query.