What is "multigraph"

Multigraph \Mul"ti*graph\, n. [Multi- + -graph.] A combined rotary type-setting and printing machine for office use. The type is transferred semi-automatically by means of keys from a type-supply drum to a printing drum. The printing may be done by means of an inked ribbon to print ``typewritten'' letters, or directly from inked type or a stereotype plate, as in a printing press.

v. print on a Multigraph machine

In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.

There are two distinct notions of multiple edges:

• Edges without own identity: The identity of an edge is defined solely by the two nodes it connects. In this case, the term "multiple edges" means that the same edge can occur several times between these two nodes.
• Edges with own identity: Edges are primitive entities just like nodes. When multiple edges connect two nodes, these are different edges.

A multigraph is different from a hypergraph, which is a graph in which an edge can connect any number of nodes, not just two.

For some authors, the terms pseudograph and multigraph are synonymous. For others, a pseudograph is a multigraph with loops.

A multigraph is a sequence of letters that behaves as a unit and is not the sum of its parts, such as English or French . The term is infrequently used, as the number of letters is usually specified:

• Digraph (two letters, as or )
• Trigraph (three letters, as or )
• Tetragraph (four letters, as German )
• Pentagraph (five letters)
• Hexagraph (six letters)
• Heptagraph (seven letters)

Combinations longer than tetragraphs are unusual. The German pentagraph has largely been replaced by , remaining only in proper names such as or . Except for doubled trigraphs like German , hexagraphs are found only in Irish vowels, where the outside letters indicate whether the neighboring consonant is " broad" or " slender". However, these sequences are not predictable. The hexagraph , for example, where the and mark the consonants as broad, represents the same sound (approximately the vowel in English write) as the trigraph , and with the same effect on neighboring consonants.

The seven-letter German sequence , used to transliterate Russian , as in for " borscht", is a sequence of a trigraph and a tetragraph rather than a heptagraph. Likewise, the Juu languages have been claimed to have a heptagraph , but this is also a sequence, of and .

Beyond the Latin alphabet, Morse code uses hexagraphs for several punctuation marks, and the dollar sign is a heptagraph, . Longer sequences are considered ligatures, and are transcribed as such in the Latin alphabet.

A multigraph is a mathematical graph where some pairs of vertices are connected by more than one edge.

Multigraph also may refer to:

• Multigraph (orthography)
• American Multigraph, corporate-merger partner with producer of addressograph machines
• Multigraph (software)