As opposed to a multigraph, a simple graph is an undirected graph that has no loops and no more
than one edge between any two different vertices.
In a simple graph the edges of the graph form a set (rather than a multiset) and
each edge is a distinct pair of vertices. In a simple graph with $n$ vertices every vertex has a degree
that is less than $n$ (the converse, however, is not true — there exist non-simple graphs with $n$ vertices
in which every vertex has a degree smaller than $n$).