Definition:Multigraph/Multiple Edge
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Definition
Let $G = \struct {V, E}$ be a multigraph.
A multiple edge is an edge of $G$ which has another edge with the same endvertices.
That is, where there is more than one edge that joins any pair of vertices, each of those edges is called a multiple edge.
Multiplicity
The multiplicity of an edge is the number of edges having the same pair of endvertices.
Also known as
A multiple edge is also known as parallel edges.
Also see
- Results about multiple edges can be found here.
Sources
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.6$: Networks as Mathematical Models
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): graph: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): graph: 2.