As LLM agents act across personal applications, web browsers, and other interfaces, their reusable skill libraries can scale to thousands of skills. This scale introduces two challenges. First, loading the full library saturates the context window, driving up token costs, hallucination, and latency. Second, semantic retrieval surfaces topically relevant skills but can miss upstream and downstream prerequisite skills, creating a prerequisite gap that leaves the retrieved bundle insufficient for execution. We present Graph-of-Skills (GoS), an inference-time structural retrieval layer for large skill libraries. GoS constructs an executable skill graph offline from skill packages, then retrieves a bounded, dependency-aware bundle through hybrid semantic-lexical seeding, reverse-aware Personalized PageRank, and context-budgeted hydration. Across SkillsBench and ALFWorld, with three model families (Claude Sonnet 4.5, MiniMax M2.7, and GPT-5.2 Codex), GoS attains the highest average reward in all six model-benchmark blocks, at a fraction of the token cost of loading the full library. On SkillsBench with GPT-5.2 Codex it raises average reward by 7.0 absolute points over full skill loading, a 25.6% relative gain, while cutting total tokens by 56.7%. Ablations isolate the mechanism: replacing reverse traversal with forward propagation costs 9.1 reward points, a larger loss than removing the graph altogether. The gain thus comes from traversing dependencies backwards, not from graph diffusion as such. A budget-matched retrieval study holding seeding, reranking, hydration, and context budget fixed reproduces the same ordering, with dependency-pair co-recovery falling from 0.654 to 0.362. Code is available at https://github.com/davidliuk/graph-of-skills

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