Knowledge graphs used by agentic systems are often treated as flat stores of extracted triples, with little record of who owns a fact, why it was admitted, or how it should be used downstream. We argue that reliable agentic knowledge systems require governance as an essential component of graph construction to bridge this gap. We propose MAGG, a principled multi-agent framework for constructing Governed Knowledge Graphs that introduces explicit governance decisions for reliable and trustworthy knowledge sharing. A domain classifier first induces entity and relation types directly from document content, enabling operation in open-world settings without fixed schemas. Candidate triples are assigned to domain owners, reviewed against supporting evidence, admitted through governance decisions, and stored with audit metadata. The same ownership structure is reused during question answering, where queries are routed to domain-specific graph experts rather than answered through undifferentiated retrieval. Our evaluation demonstrates MAGG's effectiveness: On SciERC, MAGG improves strict triple F1 by 47% and mapped triple F1 by 51% over flat insertion. A blinded review of 120 triples finds governed-only triples more often source-supported than flat-only ones, and revised triples supported in 100% of cases. Finally, on MuSiQue, MAGG outperforms Microsoft GraphRAG by 9.0 exact-match points and 11.2 token-F1 points.

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