In graph theory, multiple edges (also called parallel edges or a multi-edge), are two or more edges that are incident to the same two vertices. A simple graph has no multiple edges.
Depending on the context, a graph may be defined so as to either allow or disallow the presence of multiple edges (often in concert with allowing or disallowing loops):
- Where graphs are defined so as to allow multiple edges and loops, a graph without loops is often called a multigraph.
- Where graphs are defined so as to disallow multiple edges and loops, a multigraph or a pseudograph is often defined to mean a "graph" which can have loops and multiple edges.
Multiple edges are, for example, useful in the consideration of electrical networks, from a graph theoretical point of view.
A planar graph remains planar if an edge is added between two vertices already joined by an edge; thus, adding multiple edges preserves planarity.
A dipole graph is a graph with two vertices, in which all edges are parallel to each other.
Famous quotes containing the words multiple and/or edges:
“Combining paid employment with marriage and motherhood creates safeguards for emotional well-being. Nothing is certain in life, but generally the chances of happiness are greater if one has multiple areas of interest and involvement. To juggle is to diminish the risk of depression, anxiety, and unhappiness.”
—Faye J. Crosby (20th century)
“People stay
Next to the edges of fields, hoping that out of nothing
Something will come, and it does, but what?”
—John Ashbery (b. 1927)