Brain network analysis is crucial for understanding cognition and neurological disorders, yet existing deep learning methods mainly treat connectome analysis as a graph-to-logit classification problem, offering limited explanatory reasoning. Large language models (LLMs) provide a promising interface for knowledge-intensive scientific analysis, but directly applying general-purpose LLMs to brain networks remains challenging due to the structure-language gap, limited neuroscience grounding, and overconfident positive predictions. In this paper, we propose \textbf{BrainAgent}, an agentic LLM framework for knowledge-enhanced brain network analysis. BrainAgent reformulates connectome classification as an iterative process of topology-aware understanding, external retrieval, reasoning, and reflection. Specifically, it first converts raw brain networks into compact multi-level structural descriptions through brain-specific analysis tools, then retrieves relevant neuroscience knowledge and task-specific cases to ground the reasoning process, and finally generates structured predictions with reflective verification. Experiments on four public rs-fMRI datasets show that BrainAgent consistently improves different closed-source and open-source LLM backbones over direct prompting and standard reasoning baselines. Further ablation and interpretability analyses demonstrate the effectiveness of each component and show that BrainAgent produces more comprehensive, multi-level, and verifiable explanations.These results indicate that agentic LLMs provide a practical route toward interpretable and knowledge-grounded brain network analysis.

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