Degree of a vertex in following graph.

Question

If I have the following graph :

Should the degree of vertex $v_2$ be 1 or 2...I'm asking this because I'm not sure whether loop should be counted while considering degree...

(In my notes the definition of degree of a vertex $a$ is defined to be : the no. of edges it belongs to).

Answer 1

The degree at $v_2$ is $3$. A loop adds $2$ to the degree at that vertex. (We want each edge to add $2$ to the degree count so that the sum of all degrees in a graph is equal to twice the number of edges.)

Answer 2

An edge which is a self-loop would contribute 2 to the degree of the vertex. So $v_2$ would have degree 3. This convention is consistent with the fact that each edge contributes a total of 2 to the sum of the degrees of the vertices.