A graph is a pair of sets , so we write . is a finite set and is a set of 2-element subsets of . Though in principle can be an arbitrary set, to avoid ambiguity we require . We call the elements of the vertices and the elements of the edges of the graph.
So is a graph.
A corollary of this definition is that an edge always has to have two distinct endpoints and that there can be at most one edge between two vertices.
Sometimes it is easier to represent these sets in a drawing. Then we draw the vertices as points and the edges as lines connecting the two vertices it contains.
The graph described above can be drawn as:
In practically all cases where we are just concerned with the structure of the graph, it is not important what the set names of the vertices really are. In these cases we just draw the vertices as points, as for example here: