Cyclic dependencies are a persistent architectural smell that undermines modularity, blurs ownership, and elevates maintenance risk. While LLMs provide refactoring abilities, existing tools struggle to address smells without intervention evidence, especially under large code contexts. We introduce a multi-agent LLM framework for cyclic dependency analysis, which transforms static dependency evidence into structured, verifiable explanations of architectural entanglement. The ap- proach constructs a structural dependency graph, detects cyclic regions via strongly connected components, extracts cycles as minimal witnesses of cyclicity, then produces grounded analyses. These are produced by a hierarchical team of LLM agents that describe the position, structure, and architectural impact of each cycle, clarifying why it exists and where it can be safely resolved. These explanations, validated through experiments, support LLM-enabled refactoring. Evaluation on seven open- source Python projects shows that evidence-linked analyses can guide LLM-driven edits, reducing SCC size and improving structural quality while preserving build and test integrity.