we have any arbitrary set of numbers such that the length of the set is greater than every number in the set and sum of all the numbers in the set is even, then this forms a graph with those numbers being the degree of the each vertex respectively in the graph. is always true?

I could not find the answer to it. maybe I did not look hard enough.

explanation with example:

suppose there is a set {4, 2, 4, 6, 2, 3, 1}

here every number in the set is less than 7 (length of the set) and sum of the numbers is 22 which is even, then this set can be converted to a graph of 7 vertices with those numbers as their degrees.

(a simple graph)

can someone Please answer.