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?
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.