I'm trying to learn more about graph theory, but I'm getting confused by the initial definition:
"A graph $G = (V, E)$ is an ordered pair of finite sets. Elements of V are called vertices or nodes, and elements of $E \subseteq V^{(2)}$ are called edges or arcs. We refer to V as the vertex set of G, with E being the edge set."
I interpret this as "elements E in the subset of V are called edges". This seems to conflict with the next sentence, which defines a graph as being edges and vertices...i.e.two separate sets of things? It doesn't make intuitive sense for edges to be a kind of vertex. Whats the correct interpretation of this?