Graph-Mediated Large Language Model Systems in the Agentic Era: Reasoning, Knowledge, Retrieval, Execution, and Coordination

The paper surveys how graphs are increasingly used in large language model systems to support reasoning, knowledge grounding, retrieval, memory, execution, and multi‑agent coordination. It introduces an operation‑level taxonomy that distinguishes the function of each graph operation, the component that computes it, and how its output is subsequently used. The authors compare graph observations with external computations, analyze memory updates, and examine execution dependencies, then propose an evaluation framework that organizes benchmarks, diagnostics, and system costs, concluding with open challenges in adaptive computation, memory maintenance, and dependency‑aware recovery.