Math 2.0

Combinatorics Definition

Multigraph

Builds on Graph

Definition

A multigraph is a triple G=(V,E,r)G = (V, E, r) of a set VV of vertices, a set EE of edges, and a map rr. The map rr assigns to each edge e∈Ee \in E a set r(e)⊆Vr(e) \subseteq V of one or two vertices, the ends of ee. Two distinct edges may have the same ends. Such edges are parallel, or multiple, edges. An edge with only one end is a loop.

Remarks

Some authors do not allow loops in a multigraph, and they call a multigraph with loops a pseudograph. A graph is a multigraph without loops and without parallel edges. The Seven Bridges of Königsberg form a multigraph with 44 vertices and 77 edges.

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first.

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Graph, definition, no evidence levelGraphdefinitionMultigraph, definition, no evidence levelMultigraphdefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Graph definition
  2. Multigraph definition

Where this leads

1 page builds on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Multigraph, Undirected multigraph (edges with own identity)
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