Multiple edge

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):

Multiple edges are, for example, useful in the consideration of electrical networks, from a graph theoretical point of view. Additionally, they constitute the core differentiating feature of multidimensional networks.

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.

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