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:
“Creativity seems to emerge from multiple experiences, coupled with a well-supported development of personal resources, including a sense of freedom to venture beyond the known.”
—Loris Malaguzzi (20th century)
“You say, “It is dark.” And in truth, I did place a cloud before your sun. But do you not see how the edges of the cloud are already glowing and turning light.”
—Friedrich Nietzsche (1844–1900)