Why is a graph an ordered pair? From the source of all knowledge

a graph is an ordered pair G = (V, E) comprising a set V of vertices
  or nodes together with a set E of edges or lines, which are 2-element
  subsets of V

Why must it be an ordered pair? It seems irrelevant if you mention V or E first. Must V come first since E is made up of V?
 A: You don't even need a pair. A graph may be defined simply as a set $G$ of singleton or two-element sets. The set of vertices is then $V=\bigcup G$, while $E$ is the set of two-element members of $G$, and $G\setminus E$ is the set of isolated vertices. However, this will not do if you need to specify loops, which are edges that connect a vertex to itself, or multiple edges, although these types of edge would be regarded as illegitimate or irrelevant in the mainstream of graph theory. And of course ordered pairs are needed to define a directed graph.
A: sometimes when you transform graphs to solve problems in computer science, you need to make the edges of the original graph into the vertices of the new graph (G = (V, E) gets transformed into G' = (E, E')) and then you need to define what the new edges are.
An example would be you have a map and you need to see if there's a way to get from point point A to point B where you only take right turns. $ E' = \{(u, v) \to (v, w) | u, v, w  \in V \land (u, v) \in E \land (v, w) \in E \land \text{u to v to w form a right turn} \} $
