Editing Graph (discrete mathematics) (section)

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

* The diagram is a schematic representation of the graph with vertices <math>V = \{1, 2, 3, 4, 5, 6\}</math> and edges <math>E = \{\{1, 2\}, \{1, 5\}, \{2, 3\}, \{2, 5\}, \{3, 4\}, \{4, 5\}, \{4, 6\}\}.</math>
* In [[computer science]], directed graphs are used to represent knowledge (e.g., [[conceptual graph]]), [[finite-state machine]]s, and many other discrete structures.
* A [[binary relation]] ''R'' on a set ''X'' defines a directed graph. An element ''x'' of ''X'' is a direct predecessor of an element ''y'' of ''X'' if and only if ''xRy''.
* A directed graph can model information networks such as [[Twitter]], with one user following another.<ref name="snatwitter">{{Cite journal| volume = 3| issue = 1| last = Grandjean| first = Martin| title = A social network analysis of Twitter: Mapping the digital humanities community| journal = Cogent Arts & Humanities| date = 2016| pages = 1171458| doi = 10.1080/23311983.2016.1171458| url = https://serval.unil.ch/resource/serval:BIB_81C2C68B1DF5.P001/REF| doi-access = free| access-date = 2019-09-16| archive-date = 2021-03-02| archive-url = https://web.archive.org/web/20210302190117/https://serval.unil.ch/resource/serval:BIB_81C2C68B1DF5.P001/REF| url-status = live}}</ref><ref name="twitterwtf">Pankaj Gupta, Ashish Goel, Jimmy Lin, Aneesh Sharma, Dong Wang, and Reza Bosagh Zadeh [http://dl.acm.org/citation.cfm?id=2488433 WTF: The who-to-follow system at Twitter] {{Webarchive|url=https://web.archive.org/web/20190712002903/http://dl.acm.org/citation.cfm?id=2488433 |date=2019-07-12 }}, ''Proceedings of the 22nd international conference on World Wide Web''. {{doi|10.1145/2488388.2488433}}.</ref> 
*Particularly regular examples of directed graphs are given by the [[Cayley graph]]s of finitely-generated groups, as well as [[Schreier coset graph]]s
*In [[category theory]], every [[small category]] has an underlying directed multigraph whose vertices are the objects of the category, and whose edges are the arrows of the category.  In the language of category theory, one says that there is a [[forgetful functor]] from the [[category of small categories]] to the [[Quiver (mathematics)|category of quivers]].