Now we have a graph with one edge supported by two vertices.
When a Graph family needs to have two edges without loop, another vertex is needed.
Three vertices can support two edges.
Actually, the three vertices can support three edges without loop.
They can support six edges with loop.
Thus, in graph family a vertex can support many edges, but an edge must be supported only by one vertex (loop) or two vertices.
Teknomo, Kardi (2015) Pictorial Introduction to Graph Theory. http:\\people.revoledu.com\kardi\ tutorial\GraphTheory\