As LLM agents adopt large skill libraries, selecting the right subset becomes a structural problem rather than a similarity-matching one: skills depend on, conflict with, specialize, or duplicate one another, a structure invisible to both full enumeration and embedding similarity. We present SkillDAG, which models inter-skill relationships as a typed directed graph and exposes it to an LLM agent as an inference-time, agent-callable structural retrieval interface, queried and evolved during execution rather than baked into a fixed retrieval pipeline: each search returns vector matches, typed-edge neighbors, and conflict signals, and a propose-then-commit protocol lets the agent register execution-backed edges so the graph accumulates structure across episodes. On ALFWorld and SkillsBench with MiniMax-M2.7, SkillDAG reaches 67.1% success and 27.3% reward, exceeding the strongest reported Graph-of-Skills baseline by +12.8 and +8.6 points; the advantage ports to gpt-5.2-codex, and intrinsic SkillsBench Ret@K rises from 65.5 to 78.2 under matched queries. These gains trace to isolable mechanisms: candidate ranking that stays robust as the pool grows 10x where a fixed seeding-diffusion pipeline degrades, and set-monotone online edits that enlarge ground-truth recall without evicting prior hits.