Definition:Graph (Graph Theory)

Vertex
In the above, the vertices (singular: vertex) are the points $A, B, C, D, E, F, G$ which are marked as dots.

Edge
In the above, the edges are $AB, AE, BE, CD, CE, CF, DE, DF, FG$.

Also see

 * Definition:Null Graph: A graph whose vertex set is empty.


 * Definition:Multigraph: A graph which may have more than one edge between a given pair of vertices;
 * Definition:Loop-Graph: A graph which allows an edge to start and end at the same vertex. Such an edge is called a loop.
 * Definition:Directed Graph or Definition:Digraph: A graph in which the edges are ordered pairs of vertices.

A graph which is not a multigraph nor a loop-graph nor a directed graph can be called a simple graph if this clarification is necessary.

Also defined as
Many treatments of this subject require that $V$ is non-empty, and so do not recognise the concept of a null graph.