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Undid revision 1290491005 by Manitofigh (talk) ordered and unordered pairs are a way of representing edges with directions. They are not the only way. For instance, representing a graph as a set of pairs works very badly for mixed graphs and multigraphs and is somewhat cumbersome for graph orientations. for We should keep representation details separate from the basic idea of a graph. |
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In [[discrete mathematics]], particularly in [[graph theory]], a '''graph''' is a structure consisting of a [[Set (mathematics)|set]] of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called ''[[Vertex (graph theory)|vertices]]'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line'').<ref name=":0">{{cite book|last=Trudeau|first=Richard J.|title=Introduction to Graph Theory|year=1993|publisher=Dover Pub.|___location=New York|isbn=978-0-486-67870-2|pages=19|url=http://store.doverpublications.com/0486678709.html|edition=Corrected, enlarged republication.|access-date=8 August 2012|quote=A graph is an object consisting of two sets called its ''vertex set'' and its ''edge set''.|archive-date=5 May 2019|archive-url=https://web.archive.org/web/20190505192352/http://store.doverpublications.com/0486678709.html|url-status=live}}</ref> Typically, a graph is depicted in [[diagrammatic form]] as a set of dots or circles for the vertices, joined by lines or curves for the edges.
The edges may be directed
Graphs are the basic subject studied by graph theory. The word "graph" was first used in this sense by [[James Joseph Sylvester|J. J. Sylvester]] in 1878 due to a direct relation between mathematics and [[chemical structure]] (what he called a chemico-graphical image).<ref>See:
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