Talk:Quantum graph

Metric graphs

"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)

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

• I'm also concerned about the figure. It does not look to me as if the red dashed line is the shortest distance, although it's not clear which point is x. Deltahedron (talk) 21:21, 15 August 2014 (UTC)