A multigraphMathworldPlanetmath is a graph in which we allow more than one edge to join a pair of vertices. Two or more edges that join a pair of vertices are called parallel edges. Every graph, then, is a multigraph, but not all multigraphs are graphs. Some authors define the concept of a graph by excluding graphs with multiple edges or loops. Then if they want to consider more general graphs the multigraph is introduced. Usually, such graphs have no loops. Formally, a multigraph G=(V,E) is a pair, where E=(V(2),f) is a multiset for which f(x,x)=0 and V(2) is the set of unordered pairs of V.

A multigraph can be used to a matrix whose entries are nonnegative integers. To do this, suppose that A=(aij) is an m×n matrix of nonnegative integers. Let V=ST, where S={1,,m} and T={1,,n} and connect vertex iS to vertex jT with aij edges.

Title multigraph
Canonical name Multigraph
Date of creation 2013-03-22 11:57:57
Last modified on 2013-03-22 11:57:57
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 8
Author Mathprof (13753)
Entry type Definition
Classification msc 05C75
Synonym parallel edge
Related topic Graph
Related topic SubgraphMathworldPlanetmath
Related topic GraphHomomorphism
Related topic PseudographMathworldPlanetmath
Related topic Quiver
Related topic AxiomsOfMetacategoriesAndSupercategories