Data dependencies have been extended to graphs to characterize topological and value constraints. Existing data dependencies are defined to capture inconsistencies in static graphs. Nevertheless, inconsistencies may occur over evolving graphs and only for certain time periods. The need for capturing such inconsistencies in temporal graphs is evident in anomaly detection and predictive dynamic network analysis. This paper introduces a class of data dependencies called Temporal Graph Functional Dependencies (TGFDs). TGFDs generalize functional dependencies to temporal graphs as a sequence of graph snapshots that are induced by time intervals, and enforce both topological constraints and attribute value dependencies that must be satisfied by these snapshots. (1) We establish the complexity results for the satisfiability and implication problems of TGFDs. (2) We propose a sound and complete axiomatization system for TGFDs. (3) We also present efficient parallel algorithms to detect inconsistencies in temporal graphs as violations of TGFDs. The algorithm exploits data and temporal locality induced by time intervals, and uses incremental pattern matching and load balancing strategies to enable feasible error detection in large temporal graphs. Using real datasets, we experimentally verify that our algorithms achieve lower runtimes compared to existing baselines, while improving the accuracy over error detection using existing graph data constraints, e.g., GFDs and GTARs with 55% and 74% gain in F1-score, respectively.

Graphs are increasingly being used to model information about entities, their properties, and relationships between entities. Examples include relationships between customers, their product purchases, and inter-relationships between products. Many of these graphs are not static, and operate in dynamic data environments. Large-scale knowledge bases such as DBpedia, Yago, Wikidata, and Amazon product graphs operate in such dynamic environments, where Entities in these temporal graphs are constantly changing. Having accurate and complete information is critical for downstream decision making and fact checking. Data dependencies help us to preserve accuracy of the data and have been well studied for relational data and static graphs. However, the need for FDs is also evident for temporal graphs since they specify the semantic of the data to detect inconsistencies.

Keys for graphs incorporate the topology and value constraints needed to uniquely identify entities in a graph. They have been studied to support object identification, knowledge fusion, and social network reconciliation. Existing key constraints identify entities as the matches of a graph pattern by subgraph isomorphism, which enforce label equality on node types. These constraints can be too restrictive to characterize structures and node labels that are syntactically different but semantically equivalent. We propose a new class of key constraints, Ontological Graph Keys (OGKs) that extend conventional graph keys by ontological subgraph matching between entity labels and an external ontology. We show that the implication and validation problems for OGKs are each NP-complete. To reduce the entity matching cost, we also provide an algorithm to compute a minimal cover for OGKs. We then study the entity matching problem with OGKs, and a practical variant with a budget on the matching cost. We develop efficient algorithms to perform entity matching based on a (budgeted) Chase procedure. Using real-world graphs, we experimentally verify the efficiency and accuracy of OGK-based entity matching.