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What is the common way to specify the first node in a directed edge. Let's say I have:

$$e= \left<u,v\right>$$

How can I refer to the first node in $e$?

$e[1]$ is common in programming but what is the common notation in math world?

gt6989b
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Oren Roth
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1 Answers1

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Treating edges as vectors in $\mathbb{N}^2$, it is customary to refer to the $i$'th element of a vector $\mathbf{v}$ as $v_i$. So here you would just write $e_1$ for the first element of the edge vector "$\mathbf{e}$".

But in computer science, we typically just write this out as "node $u$ of edge $(u,v)$."

If this is for homework or a paper, just define whatever notation is convenient for you at the beginning of the document and stick to it throughout. Your readers can adapt, and if they are fussy, they will quickly let you know what the conventional notation is and you will know for next time.

ted
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  • Thanks! in the end I end up using variation of your second recommendation: "{u : u the first node of edge e}" – Oren Roth Dec 10 '17 at 14:21