Knowledge Graphs (KGs) are foundational structures in many AI applications, representing entities and their interrelations through triples. However, triple-based KGs lack the contextual information of relational knowledge, like temporal dynamics and provenance details, which are crucial for comprehensive knowledge representation and effective reasoning. Instead, \textbf{Contextual Knowledge Graphs} (CKGs) expand upon the conventional structure by incorporating additional information such as time validity, geographic location, and source provenance. This integration provides a more nuanced and accurate understanding of knowledge, enabling KGs to offer richer insights and support more sophisticated reasoning processes. In this work, we first discuss the inherent limitations of triple-based KGs and introduce the concept of contextual KGs, highlighting their advantages in knowledge representation and reasoning. We then present \textbf{KGR$^3$, a context-enriched KG reasoning paradigm} that leverages large language models (LLMs) to retrieve candidate entities and related contexts, rank them based on the retrieved information, and reason whether sufficient information has been obtained to answer a query. Our experimental results demonstrate that KGR$^3$ significantly improves performance on KG completion (KGC) and KG question answering (KGQA) tasks, validating the effectiveness of incorporating contextual information on KG representation and reasoning.

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