Editing Network theory (section)

{{short description|Study of graphs as a representation of relations between discrete objects}}
{{for multi|the theory regarding the regulation of the adaptive immune system|Immune network theory|the sociological theory|Social network}}
[[File:Small Network.png|thumb|right|A small example network with eight vertices (nodes) and ten edges (links)]]
{{Network science}}

In [[mathematics]], [[computer science]] and [[network science]], '''network theory''' is a part of [[graph theory]]. It defines '''networks''' as [[Graph (discrete mathematics)|graphs]] where the vertices or edges possess attributes. Network theory analyses these networks over the [[symmetric relation]]s or [[directed graph|asymmetric relations]] between their (discrete) components.

Network theory has applications in many disciplines, including [[statistical physics]], [[particle physics]], computer science, [[electrical engineering]],<ref name="10.3390/en11061381" /><ref name="ieeexplore_8191215" /> [[biology]],<ref>{{cite journal | vauthors = Habibi I, Emamian ES, Abdi A | title = Quantitative analysis of intracellular communication and signaling errors in signaling networks | journal = BMC Systems Biology | volume = 8 | pages = 89 | date = August 2014 | pmid = 25115405 | pmc = 4255782 | doi = 10.1186/s12918-014-0089-z | doi-access = free }}</ref> [[archaeology]],<ref>{{Cite book | vauthors = Sindbæk S |title=Networks and nodal points: the emergence of towns in early Viking Age Scandinavia - Antiquity 81(311) |publisher=Cambridge University Press |year=2007 |pages=119–132 |language=English}}</ref> [[linguistics]],<ref name = Paradowskietal2021a>{{cite journal |last1=Paradowski |first1=M. B. |last2=Jarynowski |first2=A. |last3=Jelińska |first3=M. |last4=Czopek |first4=K. |title=Selected poster presentations from the American Association of Applied Linguistics conference, Denver, USA, March 2020: Out-of-class peer interactions matter for second language acquisition during short-term overseas sojourns: The contributions of Social Network Analysis |journal=Language Teaching |date=2021 |volume=54 |issue=1 |pages=139–143 |doi=10.1017/S0261444820000580 |doi-access=free }}</ref><ref name=Paradowskietal2021b>{{cite book|author1=Paradowski, M. B. |author2=Jarynowski, A. |author3=Czopek, K. |author4=Jelińska, M. |chapter=Peer interactions and second language learning: The contributions of Social Network Analysis in Study Abroad vs At-Home environments|editor1=Mitchell, Rosamond |editor2=Tyne, Henry |title=Language, Mobility and Study Abroad in the Contemporary European Context |publisher=Routledge |location=New York|year=2021|isbn=978-10-03087-95-3|pages=99–116|doi=10.1017/S0261444820000580 |s2cid=228863564 |chapter-url=https://doi.org/10.4324/9781003087953-8|display-authors=etal}}</ref><ref name = Paradowskietal2022>{{cite journal |last1= Paradowski |first1=M. B. |last2=Cierpich-Kozieł |first2=A. |last3=Chen |first3=C.-C. |last4=Ochab |first4=J. K. |title=How output outweighs input and interlocutors matter for study-abroad SLA: Computational Social Network Analysis of learner interactions |journal=The Modern Language Journal |date=2022 |volume=106 |issue=4 |pages=694–725 |doi=10.1111/modl.12811 |s2cid=255247273 |url=https://www.repository.cam.ac.uk/handle/1810/344876 }}</ref> [[economics]], [[finance]], [[operations research]], [[climatology]], [[ecology]], [[public health]],<ref>{{cite journal | vauthors = Harris JK, Luke DA, Zuckerman RB, Shelton SC | title = Forty years of secondhand smoke research: the gap between discovery and delivery | journal = American Journal of Preventive Medicine | volume = 36 | issue = 6 | pages = 538–548 | date = June 2009 | pmid = 19372026 | doi = 10.1016/j.amepre.2009.01.039 | oclc = 5899755895 }}</ref><ref>{{Cite journal| vauthors = Varda DM, Forgette R, Banks D, Contractor N |date=2009|title=Social Network Methodology in the Study of Disasters: Issues and Insights Prompted by Post-Katrina Research|journal=Population Research and Policy Review|language=en|volume=28|issue=1|pages=11–29|issn=0167-5923|oclc=5659930640|doi=10.1007/s11113-008-9110-9|s2cid=144130904}}</ref><ref>{{cite journal | vauthors = Sunkersing D, Martin FC, Sullivan P, Bell D | title = Care and support networks of community-dwelling frail individuals in North West London: a comparison of patient and healthcare workers' perceptions | journal = BMC Geriatrics | volume = 22 | issue = 1 | pages = 953 | date = December 2022 | pmid = 36494627 | pmc = 9737751 | doi = 10.1186/s12877-022-03561-y | doi-access = free }}</ref> [[sociology]],<ref>{{Cite book | vauthors = della Porta D, Diani M |title=Social Movements 2e: An Introduction  |publisher=Wiley-Blackwell |year=2010 |isbn=978-1-4051-0282-7 |edition=2nd |language=English}}</ref> [[psychology]],<ref name="Paradowski2023">{{cite journal | last1 = Paradowski | first1 = M. B. | last2 = Jelińska | first2 = M. | year = 2023 | title = The predictors of L2 grit and their complex interactions in online foreign language learning: Motivation, self-directed learning, autonomy, curiosity, and language mindsets | journal = [[Computer Assisted Language Learning]] | volume = 37 | issue = 8 | pages = 2320–2358 | doi=10.1080/09588221.2023.2192762| doi-access = free }}</ref> and [[neuroscience]].<ref>{{cite journal | vauthors = Bassett DS, Sporns O | title = Network neuroscience | journal = Nature Neuroscience | volume = 20 | issue = 3 | pages = 353–364 | date = February 2017 | pmid = 28230844 | pmc = 5485642 | doi = 10.1038/nn.4502 }}</ref><ref name="AlexF" /><ref name="10.1038/s41598-021-81767-7">{{cite journal | vauthors = Saberi M, Khosrowabadi R, Khatibi A, Misic B, Jafari G | title = Topological impact of negative links on the stability of resting-state brain network | journal = Scientific Reports | volume = 11 | issue = 1 | pages = 2176 | date = January 2021 | pmid = 33500525 | pmc = 7838299 | doi = 10.1038/s41598-021-81767-7 | bibcode = 2021NatSR..11.2176S }}</ref> Applications of network theory include [[Logistics|logistical]] networks, the [[World Wide Web]], [[Internet]], [[gene regulatory network]]s, metabolic networks, [[social networks]], [[epistemological]] networks, etc.; see [[List of network theory topics]] for more examples.

[[Euler]]'s solution of the [[Seven Bridges of Königsberg|Seven Bridges of Königsberg problem]] is considered to be the first true proof in the theory of networks.