Effective document-level machine translation (DocMT) requires capturing long-range discourse dependencies. Recent work has explored retrieval-based and discourse-aware context selection. However, these approaches often lack an explicit mechanism for modeling structured discourse dependencies between distant paragraphs in a document. In this paper, we propose G²C-MT (Graph-Guided Context for Machine Translation), which views DocMT context selection as a structured path discovery problem on a lightweight discourse graph, rather than retrieving unstructured context sets or relying on expensive LLM-based discourse modeling. In detail, we represent each paragraph as a node and model the relationship between each pair of nodes, considering their semantic similarity, adjacency, and keyword overlap. Furthermore, we propose a depth-biased random walk over the graph to sample a backward context path for each target paragraph. The context path will be used to prompt a large language model (LLM) for translation. This framework naturally supports multi-path context sampling, which can improve robustness by aggregating diverse translation candidates for discourse-ambiguous inputs. Experiments conducted across various domains show that G²C-MT outperforms strong baselines on multiple LLMs, including DeepSeek-V3, Gemini-2.5-Flash-lite, and the Qwen-2.5/3 series.