Anti-vertex for neighborhood constraints in subgraph queries

This paper focuses on subgraph queries where constraints are present in the neighborhood of the explored subgraphs. We describe anti-vertex, a declarative construct that indicates absence of a vertex, i.e., the resulting subgraph should not have a vertex in its specified neighborhood that matches the anti-vertex. We formalize the semantics of anti-vertex to benefit from automatic reasoning and optimization, and to enable standardized implementation across query languages and runtimes. The semantics are defined for various matching semantics that are commonly employed in subgraph querying (isomorphism, homomorphism, and no-repeated-edge matching) and for the widely adopted property graph model. We illustrate several examples where anti-vertices can be employed to help familiarize with the anti-vertex concept. We further showcase how anti-vertex support can be added in existing graph query languages by developing prototype extensions of Cypher language. Finally, we study how anti-vertices interact with the symmetry breaking technique in subgraph matching frameworks so that their meaning remains consistent with the expected outcome of constrained neighborhoods to connected vertices.