Path-based Algebraic Foundations of Graph Query Languages

Graph databases are gaining momentum thanks to the flexibility and expressiveness of their data model and query languages. A standardization activity driven by the ISO/IEC standardization body is also ongoing and has already conducted to the specification of the first versions of two standard graph query languages, namely SQL/PGQ and GQL, respectively in 2023 and 2024. Apart from the standards, there exists a panoply of concrete graph query languages in commercial and open-source graph databases, each of which exhibits different features and modes. In this paper, we tackle the heterogeneity problem of graph query languages by laying the foundations of a unifying path-oriented algebraic framework. Such a theoretical framework is currently missing in the graph databases landscape, thus impeding a lingua franca in which different graph query language implementations can be expressed and cross-compared. Our framework gives a blueprint for correct implementation of graph queries of different expressiveness. It allows to overcome the boundaries of current versions of standard query languages, thus paving the way to future extensions including query composability. It also allows, when the path-based semantics is stripped off, to express classical Codd's relational algebra enhanced with a recursive operator, thus proving its utility for a wide range of queries in database management systems.