define simple graph
A simple graph, as opposed to a multigraph, is an undirected graph in which both multiple edges and loops are disallowed. In a simple graph the edges form a set (rather than a multiset) and each edge is an unordered pair of distinct vertices.
Informally, a graph is a finite set of dots called vertices (or nodes) connected by links called edges (or arcs). More formally: a simple graph is a (usually finite) set of vertices V and set of unordered pairs of distinct elements of V called edges. Not all graphs are simple.