Content deleted Content added
mNo edit summary |
Added context on graph theory Tag: Reverted |
||
Line 7:
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.
Graph theory is the theoretical foundation of [[network science]], which is the application of graph theory to various real-life domains of applications (social, biological, power grid networks...)<ref name=barabasi_network>{{cite book
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:▼
| last1=Barabási
| first1=Albert-László
| last2=Pósfai
| first2=Márton
| author-link1=Albert-László Barabási
| date=2016
| title=Network science
| url=http://networksciencebook.com/
| ___location=Cambridge, United Kingdom
| publisher=Cambridge University Press
| page=456
| isbn=978-1-107-07626-6}}</ref>
Graphs are the basic subject studied by graph theory.
The origins of graph theory dates back to the mid 18th century with the [[Seven Bridges of Königsberg| bridges of Königsberg]] problem<ref name=barabasi_network></ref>, solved by [[Leonhard Euler]] using a mathematical proof that is considered to be the first to use the tools of graph theory<ref>{{cite journal
| last1 = Euler
| first1 = Leonhard
| author-link1=Leonhard Euler
| date = 1741
| title = Solutio problematis ad geometriam situs pertinentis
| url = https://archive.org/details/commentariiacade08impe/page/128/mode/2up
| journal = Commentarii academiae scientiarum Petropolitanae
| pages = 128-140
| access-date = 2024-09-21
}} English translation available at https://www.cantab.net/users/michael.behrend/repubs/maze_maths/pages/euler.html</ref>.
▲
* J. J. Sylvester (February 7, 1878) [https://books.google.com/books?id=KcoKAAAAYAAJ&q=Sylvester&pg=PA284 "Chemistry and algebra"], {{Webarchive|url=https://web.archive.org/web/20230204142956/https://books.google.com/books?id=KcoKAAAAYAAJ&vq=Sylvester&pg=PA284 |date=2023-02-04 }} ''Nature'', ''17'' : 284. {{doi|10.1038/017284a0}}. From page 284: "Every invariant and covariant thus becomes expressible by a ''graph'' precisely identical with a Kekuléan diagram or chemicograph."
* J. J. Sylvester (1878) [https://books.google.com/books?id=1q0EAAAAYAAJ&pg=PA64 "On an application of the new atomic theory to the graphical representation of the invariants and covariants of binary quantics, – with three appendices"], {{Webarchive|url=https://web.archive.org/web/20230204142957/https://books.google.com/books?id=1q0EAAAAYAAJ&pg=PA64 |date=2023-02-04 }} ''American Journal of Mathematics, Pure and Applied'', ''1'' (1) : 64–90. {{doi|10.2307/2369436}}. {{JSTOR|2369436}}. The term "graph" first appears in this paper on page 65.</ref><ref>{{Cite book
| |||