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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]] or a [[multigraph|01M5T0KDG7]].\nAn Eulerian trail of $G$ is a [[trail|062MQGP8M5]] in $G$ that uses every edge of $G$ exactly once.\nAn Eulerian circuit is an Eulerian trail that starts and ends at the same vertex.\n\n## Remarks\n\nA graph with an Eulerian circuit is called Eulerian.\n[[Euler's theorem|020422MDQF]] characterizes the connected graphs with an Eulerian circuit by the parity of the degrees.\nThe [[Seven Bridges of Königsberg|0YCW781Q9D]] form a multigraph with no Eulerian trail.\n\n## Explanations\n\n### L1 human\n\nAn Eulerian trail draws the whole graph in one stroke, without lifting the pen and without going over any line twice.\nAn Eulerian circuit also ends where it starts.\n",
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