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The most basic abstraction in Apache Spark is the Resilient Distributed Dataset (RDD). RDDs are the foundational data structure in Spark, designed to handle distributed data in a fault-tolerant manner. They represent an immutable distributed collection of objects that can be processed in parallel across a cluster of computers. This abstraction is critical for enabling Spark's capability to perform distributed computing efficiently and effectively.

RDDs allow users to perform transformations and actions on data in a distributed fashion, leveraging Spark's powerful processing engine to manage the complexities of fault tolerance and data persistence. They provide a low-level API that gives developers control over data partitioning and persistence, making them suitable for a wide range of data processing applications.

In contrast, while DataFrames and Datasets build upon RDDs and provide higher-level abstractions with optimizations for structured data, they ultimately rely on RDDs for their underlying implementations. Graph is also a conceptual structure used for specific applications, but it does not serve as the foundational abstraction like RDDs do. Understanding RDDs is crucial for developers working with Apache Spark, as they lay the groundwork for more advanced features and abstractions in the framework.