Graph (discrete mathematics): Difference between revisions

Revision as of 11:06, 14 April 2024

Revision as of 11:07, 14 April 2024

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[[File:6n-graf.svg|thumb|A graph with six vertices and seven edges]]

In [[discrete mathematics]], and more specifically in [[graph theory]], a '''graph''' is a structure amounting to a [[Set (mathematics)|set]] of objects in which 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'' doror ''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 or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then this graph is directed, because owing money is not necessarily reciprocated.