Notation for length of path in a graph

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What is the notation for the length (number of edges) of a path P in a graph?

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Notation is not unique. If you are the writer, you can choose your own. For example, if $P$ is the name of a path, you could call its length $|P|$, or $\#P$, or $l(P)$, or $\operatorname{length}(P)$. Just define the notation explicitly.