Message passing neural networks have recently evolved into a state-of-the-art approach to representation learning on graphs. Existing methods perform synchronous message passing along all edges in multiple subsequent rounds and consequently suffer from various shortcomings: Propagation schemes are inflexible since they are restricted to k-hop neighborhoods and insensitive to actual demands of information propagation. Further, long-range dependencies cannot be modeled adequately and learned representations are based on correlations of fixed locality. These issues prevent existing methods from reaching their full potential in terms of prediction performance. Instead, we consider a novel asynchronous message passing approach where information is pushed only along the most relevant edges until convergence. Our proposed algorithm can equivalently be formulated as a single synchronous message passing iteration using a suitable neighborhood function, thus sharing the advantages of existing methods while addressing their central issues. The resulting neural network utilizes a node-adaptive receptive field derived from meaningful sparse node neighborhoods. In addition, by learning and combining node representations over differently sized neighborhoods, our model is able to capture correlations on multiple scales. We further propose variants of our base model with different inductive bias. Empirical results are provided for semi-supervised node classification on five real-world datasets following a rigorous evaluation protocol. We find that our models outperform competitors on all datasets in terms of accuracy with statistical significance. In some cases, our models additionally provide faster runtime.

This paper studies a class of neighborhood con-straints to characterize and repair erroneous entity information in multi-relational graph data. (1) We propose a class of constraints called star functional dependencies (StarFDs). Unlike conventional integrity constraints, a StarFDenforces value dependencies conditioned by entities and their relevant neighbors, which are identified by a star pattern that incorporates conjunctive regular path queries. StarFDsachieve a balance between expressiveness and complexity: the validation of StarFDsis tractable, and the satisfiability and implication of StarFDsare NP-complete and coNP-complete, respectively. (2) Given a set of StarFDsΣ and a graph G, the entity repair problem is to compute a minimum repair of G by enforcing Σ with the smallest amount of changes. Although this problem is NP-complete and hard to approximate, we show it is feasible to compute repairs in large graphs. Our approach (a) discriminately detects and resolves errors with optimal, approximable and cost-bounded solutions whenever possible, and (b) incurs a time cost determined by Σ and the size of inconsistencies, for all cases. Using real world data, we show that StarFD-based techniques effectively identify and repair errors. We also show that our repairing algorithms benefit other tasks such as fact checking.

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.