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.

中文翻译：

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图的依赖关系

本文提出了一类图的依赖关系，简称图实体依赖关系（GED）。GED 被定义为图形模式和属性依赖项的组合。在统一的格式中，GED 可以用常量字面量表示图函数依赖关系以捕捉不一致，并使用带有 id 字面量的键来识别图中的实体（顶点）。我们修改了对 GED 的追逐并证明了它的 Church-Rosser 属性。我们描述了 GED 的可满足性和含义，并确定了这些问题的复杂性以及 GED 的验证问题，在存在和不存在常量文字和 id 文字的情况下。我们还为 GED 的有限蕴涵开发了一个健全、完整和独立的公理系统。此外，我们使用内置谓词或析取来扩展 GED，以在表达能力和复杂性之间取得平衡。我们解决了可满足性、含义的复杂性，