Definition:Simple Graph

Definition
A simple graph is a graph which is:


 * An undirected graph, that is, the edges are defined as doubleton sets of vertices and not ordered pairs


 * Not a multigraph, that is, there is no more than one edge between each pair of vertices


 * Not a loop-graph, that is, there are no loops, that is, edges which start and end at the same vertex


 * Not a weighted graph, that is, the edges are not mapped to a number.

Also defined as
Some sources impose the condition that a (simple) graph must have at least one vertex.

Some sources also define a (simple) graph as one which has a finite number of vertices.