State-of-the-art link prediction (LP) models demonstrate impressive benchmark results. However, popular benchmark datasets often assume that training, validation, and testing samples are represen- tative of the overall dataset distribution. In real-world situations, this assumption is often incorrect; uncontrolled factors lead new dataset samples to come from a different distribution than train- ing samples. Additionally, the majority of recent work with graph dataset shift focuses on node- and graph-level tasks, largely ignor- ing link-level tasks. To bridge this gap, we introduce a novel splitting strategy, known as LPShift, which utilizes structural properties to induce a controlled distribution shift. We verify LPShift's effect through empirical evaluation of SOTA LP models on 16 LPShift variants of original dataset splits, with results indicating drastic changes to model performance. Additional experiments demon- strate graph structure has a strong influence on the success of current generalization methods. The source code is available here https://github.com/revolins/LPShift.

Knowledge Graph Completion (KGC) attempts to predict missing facts in a Knowledge Graph (KG). Recently, there's been an increased focus on designing KGC methods that can excel in the inductive setting, where a portion or all of the entities and relations seen in inference are unobserved during training. Numerous benchmark datasets have been proposed for inductive KGC, all of which are subsets of existing KGs used for transductive KGC. However, we find that the current procedure for constructing inductive KGC datasets inadvertently creates a shortcut that can be exploited even while disregarding the relational information. Specifically, we observe that the Personalized PageRank (PPR) score can achieve strong or near SOTA performance on most datasets. In this paper, we study the root cause of this problem. Using these insights, we propose an alternative strategy for constructing inductive KGC datasets that helps mitigate the PPR shortcut. We then benchmark multiple popular methods using the newly constructed datasets and analyze their performance. The new benchmark datasets help promote a better understanding of the capabilities and challenges of inductive KGC by removing any shortcuts that obfuscate performance. The code and dataset and can be found https://github.com/HarryShomer/Better-Inductive-KGC.

Recent studies suggest that large language models (LLMs) possess the capability to solve graph reasoning tasks. Notably, even when graph structures are embedded within textual descriptions, LLMs can still effectively answer related questions. This raises a fundamental question: How can a decoder-only Transformer architecture understand underlying graph structures? To address this, we start with the substructure extraction task, interpreting the inner mechanisms inside the transformers and analyzing the impact of the input queries. Specifically, through both empirical results and theoretical analysis, we present Induced Substructure Filtration (ISF), a perspective that captures the substructure identification in the multi-layer transformers. We further validate the ISF process in LLMs, revealing consistent internal dynamics across layers. Building on these insights, we explore the broader capabilities of Transformers in handling diverse graph types. Specifically, we introduce the concept of thinking in substructures to efficiently extract complex composite patterns, and demonstrate that decoder-only Transformers can successfully extract substructures from attributed graphs, such as molecular graphs. Together, our findings offer a new insight on how sequence-based Transformers perform the substructure extraction task over graph data.