If between two adjacent vertices then in 2-dimensions it is a side, in 3-d and edge.
If between non-adjacent vertices, a diagonal.
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I guess you mean "A line drawn between 2 vertices which are not next to each other?":The line is a diagonal.
a draipipe
It could be a diagonal line of a polygon with more than 3 sides
N-2 according to yahoo answers
A diagonal.