Dependencies for Graphs

This article proposes a class of dependencies for graphs, referred to as graph entity dependencies (GEDs). A GED is defined as a combination of a graph pattern and an attribute dependency. In a uniform format, GEDs can express graph functional dependencies with constant literals to catch inconsistencies, and keys carrying id literals to identify entities (vertices) in a graph. We revise the chase for GEDs and prove its Church-Rosser property. We characterize GED satisfiability and implication, and establish the complexity of these problems and the validation problem for GEDs, in the presence and absence of constant literals and id literals. We also develop a sound, complete and independent axiom system for finite implication of GEDs. In addition, we extend GEDs with built-in predicates or disjunctions, to strike a balance between the expressive power and complexity. We settle the complexity of the satisfiability, implication, and validation problems for these extensions.