A random graph consisting of n vertices and k undirected edges is constructed by repeating the following step k times:
Randomly choose 2 vertices without replacement from n vertices, and connect them with an edge.
What is the expected degree of a vertex?
I know that expected value is calculated by the probability*degree, but I'm not sure how to make a general case when we have n vertices and k undirected edges. Can someone make this problem easier to understand by explaining how the expected value is related to the problem statement? How can I generalize other problems of the same form?