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

Which of the following statements about evolving networks is FALSE?

a) In the Barabási–Albert (BA) model, new nodes are added to the network with a preference for connecting to high-degree nodes.

b) The Erdős-Rényi random network model grows by adding nodes over time, similar to the BA model.

c) In evolving networks, the degree distribution can change as new nodes and edges are added.

d) In the BA model, the probability of a new node connecting to existing nodes is uniform across all nodes.

e) None of the above.