AgenticGNN: A Spectral-Inspired Agentic Framework for Automated Graph Learning Algorithm Design

Existing large language model (LLM)-based frameworks for automated graph learning algorithm design typically rely on static performance feedback to conduct black-box iterative optimization. Consequently, they fail to establish explicit associations between target-graph features and algorithm design principle, leading to suboptimal performance and poor cross-task knowledge transfer. Inspired by spectral graph theory, which reveals the intrinsic filtering behaviors of graph learning operators via spectral energy changes, we propose AgenticGNN, an agentic framework for automated graph learning algorithm design that integrates multi-level graph feature perception, adaptive spectral-theory-guided context construction, and spectral-aware evolutionary feedback. AgenticGNN first quantifies target-graph characteristics at the neighborhood, community, and global-topology levels, and translates these measurements into an adaptive natural-language context informed by spectral graph theory. This context guides an LLM to generate candidate graph learning algorithms through structured reasoning. During iterative evolution, AgenticGNN analyzes spectral changes to attribute the effects of design decisions on model behavior. The resulting graph features, design rationales, generated code, and evaluation outcomes are distilled into a progressively evolving knowledge base, enabling explicit and reusable mappings from graph characteristics to algorithm design strategies. Experimental results on nine real-world datasets demonstrate that AgenticGNN consistently outperforms state-of-the-art automated design baselines, achieving superior task performance, higher design efficiency, and robust cross-task generalization. The source code is available at https://anonymous.4open.science/r/AgenticGNN-FDCC.