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Talk:Quantum graph

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Metric graphs

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"It is possible to embed a metric graph in the plane" cannot be correct in general. Embedding in any Euclidean space would need the edge lengths to satisfy the triangle inequality, which is not stated as a requirement in the definition. Saying "if the lengths are chosen appropriately" is nonsense: the edge lengths are part of the data of the graph. Deltahedron (talk) 19:54, 15 August 2014 (UTC)[reply]

A metric graph embedded in the plane with three open edges. The dashed line denotes the metric distance between two points and .