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:
“There is a continual exchange of ideas between all minds of a generation. Journalists, popular novelists, illustrators, and cartoonists adapt the truths discovered by the powerful intellects for the multitude. It is like a spiritual flood, like a gush that pours into multiple cascades until it forms the great moving sheet of water that stands for the mentality of a period.”
—Auguste Rodin (1849–1917)
“I always used to suffer a great deal if I let myself get too close to reality since the definitive world of the everyday with its hard edges and harsh light did not have enough resonance to echo the demands I made upon experience. It was as if I never experienced experience as experience. Living never lived up to the expectations I had of it—the Bovary syndrome.”
—Angela Carter (1942–1992)