Most automated survey generation systems retrieve papers as flat documents, limiting their ability to capture research structure. We present SurveyGraph, a framework built around a Methods-Entity Knowledge Graph (MEKG) encoding method-level follow-on, competition, and shared-resource relations. The graph supports core-paper discovery, retrieval, hybrid outlining, and evidence-gated narrative synthesis. We evaluate retrieval, semantic edges, citation grounding, collection coverage, and generation-stage components. In a controlled seven-method equal-budget benchmark, MEKG-anchored fusion balances recall and structural density, with an independent co-citation check. In a separate archived graph-native diagnostic, graph-aware retrieval nearly doubles recall over flat lexical baselines across eight runs (p = 0.004). A semantic evidence gate achieves AUC = 0.75. Audits of 160 generated sentences find 80.6% anchored-or-partial citation support. Human adjudication of 108 stratified semantic edges finds 68.5% supported-or-partial relations (binary-support Cohen's kappa = 0.64), with improves strongest (80.6%) and extends weakest (52.8%). A SurveyBench-facing collection probe reaches mean reference coverage of 0.521 across four topics with an eight-paper budget. Same-backend Qwen diagnostics on a 30-paper/74-relation graph show reduced organization signals when hybrid outlining is removed. Concurrent-system comparisons provide bounded context rather than matched-backend end-to-end evidence. The results position MEKG as an auditable structural layer for typed diagnostics, relation-specific filtering, and controlled survey generation. Code and artifacts: https://github.com/xzzvsxd/SurveyGraph.

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