Backdoor detection for large language models is increasingly difficult in realistic black-box settings, where defenders lack access to weights, gradients, training data, or attack-specific trigger mechanisms. Existing detectors often rely on white-box signals, labeled poisoned data, or output-level signatures, making them brittle against inference-time and non-training-based attacks on closed-source models. We propose GCoTD, a black-box detector that identifies backdoors by analyzing the structure of an LLM’s reasoning rather than its final outputs alone. GCoTD retrieves few-shot graph Chain-of-Thought templates to elicit graph-structured reasoning traces from the target model, then applies a lightweight language-model detector to distinguish clean from poisoned reasoning patterns. By representing reasoning as graphs, GCoTD captures mechanism-agnostic irregularities such as logic discontinuities, isolated subchains, and inconsistent intermediate transitions, without requiring access to model internals or training data. Experiments across four attack types and six LLMs, including LLaMA-3, DeepSeek-V3, Qwen-3, and GPT-class models, show that GCoTD outperforms recent black-box baselines and retains strong detection performance on held-out attacks.