Consider a simple, undirected graph $G$ with n vertices and $m$ edges. Let $d(v)$ denote the degree of vertex v in $G$. The degree distribution of $G$ is the probability distribution $P(k)$ that a randomly selected vertex has degree $k$. Which of the following statements is true regarding the degree distribution of a simple graph?

a) For any simple graph with $n$ vertices and $m$ edges, the sum of the degrees of all vertices is equal to $n+m$.

b) In any simple graph, the degree distribution $P(k)$ is always uniform, meaning all vertices have the same degree.

c) In a simple graph, the degree distribution $P(k)$ must sum to 1 when considering all possible degrees $k$.

d) If a simple graph is connected, its degree distribution must be a normal distribution.

e) None of above