multigraph
A multigraph 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 is a pair, where
is a multiset for which and is the set of unordered pairs
of .
A multigraph can be used to a matrix whose entries are nonnegative integers. To do this, suppose that is an matrix of nonnegative integers. Let , where and and connect vertex to vertex with 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 | Subgraph![]() |
Related topic | GraphHomomorphism |
Related topic | Pseudograph![]() |
Related topic | Quiver |
Related topic | AxiomsOfMetacategoriesAndSupercategories |