Wikipedia states the following about Cayley graphs:
The Cayley graph Γ(G,S) depends in an essential way on the choice of the set S of generators. For example, if the generating set S has k elements then each vertex of the Cayley graph has k incoming and k outgoing directed edges. In the case of a symmetric generating set S with r elements, the Cayley graph is a regular directed graph of degree r.
I understand the first case, where a generating set S of k elements creates a 2k-regular graph. But:
What is a symmetric generating set S of r elements?
How can it create a r-regular graph?