How are loops represented in an edge set?

Question

When a node $v_1$ in a graph has an edge to itself (a loop), will this be represented as $\{v_1\}$ or as $\{v_1, v_1\}$?

Answer 1

Loops are represented within the edge set as:

$$\{v_1,v_1\}\in\large\bf\epsilon$$

$\{v_1\}$ would be meaningless as a vertex cannot be an edge, as an edge requires $2$ vertices.