Edges connect various vertices of a graph together and represent the relationship between themselves. In addition to simple edges, they can be of the following special types:

• Self-edge: Sometimes, a particular vertex can have a relationship with itself. For example, John transfers money from his business account to his personal account. Such a special relationship can be represented by a self-directed edge.
• Hyperedge: Sometimes, more than one vertex is connected by the same edge. An edge that connects more than one vertex to represent such a relationship is called a hyperedge. For example, suppose all three of Mike, John, and Sarah are working on one specific project.

A diagram of a self-edge and hyperedge graph is shown here:

Note that one particular graph can have more than one special type of edge node. This means that one particular graph can have both self-edges and hyper edges at the same time.