why in every graph the sum of the degrees of all the vertices equals twice the number of edges?

Question

trying to figure out if this is true, and why?

Answer 1

It is not true.

The sum of the degrees in a triangle (on a flat surface) is 180.

The number of edges in a triangle is 3, twice that number would be 6.

6 does not equal 180.

Comments

The degree of a vertices is how many edges are coming out of it. So, for a triangle, the sum of the degrees of a triangle is 180, but the sum of the degrees of the vertices of a triangle is (2+2+2) 6. Being that there are 3 edges, the sum of the degrees of the vertices (6) is exactly double the number of edges.

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Looked it up...graph theory.  Was thinking geometry due to the category the question was posted in.  I stand corrected.

The sum degrees of all the vertices would be twice the number of edges because each edge has to have a start and an end.  Introducing 1 edge introduces 2 endpoints, which makes 2 degrees.

Answer 2

Every edge is connected to exactly two vertices.