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

Graphs play an increasingly important role in large language model (LLM) systems, supporting structural reasoning, knowledge grounding, retrieval, and memory. As these systems evolve toward the agentic era, graphs also organize execution dependencies and multi-agent communication, linking intermediate observations and retained information to subsequent decisions. However, understanding their contribution requires distinguishing the function of each graph operation, the component responsible for its computation, and the subsequent use of its output. This survey introduces an operation-level role--locus taxonomy for reasoning, knowledge and evidence, retrieval and memory, execution, and coordination. We compare how graph observations and external computations guide decisions, how memory representations and updates support later tasks, and how dependencies constrain execution and information delivery. These comparisons distinguish improvements in local metrics from downstream task performance while retaining the conditions under which results were reported. We then organize benchmarks, comparison designs, process diagnostics, and system costs into an evaluation framework. Finally, we identify open challenges in adaptive computation and stopping, memory maintenance, and dependency-aware recovery. The survey provides a basis for assessing when graph mechanisms are useful and for evaluating their effects across components and stages.