\begin{definition}[Definition:Simple Graph]
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.
\end{definition}