Network theory

A small example network with eight vertices (nodes) and ten edges (links)

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

Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering,^[1]^[2] biology,^[3] archaeology,^[4] linguistics,^[5]^[6]^[7] economics, finance, operations research, climatology, ecology, public health,^[8]^[9]^[10] sociology,^[11] psychology,^[12] and neuroscience.^[13]^[14]^[15] Applications of network theory include logistical networks, the World Wide Web, Internet, gene regulatory networks, 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 problem is considered to be the first true proof in the theory of networks.

^ Cite error: The named reference 10.3390/en11061381 was invoked but never defined (see the help page).
^ Cite error: The named reference ieeexplore_8191215 was invoked but never defined (see the help page).
^ Habibi I, Emamian ES, Abdi A (August 2014). "Quantitative analysis of intracellular communication and signaling errors in signaling networks". BMC Systems Biology. 8: 89. doi:10.1186/s12918-014-0089-z. PMC 4255782. PMID 25115405.
^ Sindbæk S (2007). Networks and nodal points: the emergence of towns in early Viking Age Scandinavia - Antiquity 81(311). Cambridge University Press. pp. 119–132.
^ Paradowski, M. B.; Jarynowski, A.; Jelińska, M.; Czopek, K. (2021). "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". Language Teaching. 54 (1): 139–143. doi:10.1017/S0261444820000580.
^ Paradowski, M. B.; Jarynowski, A.; Czopek, K.; Jelińska, M.; et al. (2021). "Peer interactions and second language learning: The contributions of Social Network Analysis in Study Abroad vs At-Home environments". In Mitchell, Rosamond; Tyne, Henry (eds.). Language, Mobility and Study Abroad in the Contemporary European Context. New York: Routledge. pp. 99–116. doi:10.1017/S0261444820000580. ISBN 978-10-03087-95-3. S2CID 228863564.
^ Paradowski, M. B.; Cierpich-Kozieł, A.; Chen, C.-C.; Ochab, J. K. (2022). "How output outweighs input and interlocutors matter for study-abroad SLA: Computational Social Network Analysis of learner interactions". The Modern Language Journal. 106 (4): 694–725. doi:10.1111/modl.12811. S2CID 255247273.
^ Harris JK, Luke DA, Zuckerman RB, Shelton SC (June 2009). "Forty years of secondhand smoke research: the gap between discovery and delivery". American Journal of Preventive Medicine. 36 (6): 538–548. doi:10.1016/j.amepre.2009.01.039. OCLC 5899755895. PMID 19372026.
^ Varda DM, Forgette R, Banks D, Contractor N (2009). "Social Network Methodology in the Study of Disasters: Issues and Insights Prompted by Post-Katrina Research". Population Research and Policy Review. 28 (1): 11–29. doi:10.1007/s11113-008-9110-9. ISSN 0167-5923. OCLC 5659930640. S2CID 144130904.
^ Sunkersing D, Martin FC, Sullivan P, Bell D (December 2022). "Care and support networks of community-dwelling frail individuals in North West London: a comparison of patient and healthcare workers' perceptions". BMC Geriatrics. 22 (1): 953. doi:10.1186/s12877-022-03561-y. PMC 9737751. PMID 36494627.
^ della Porta D, Diani M (2010). Social Movements 2e: An Introduction (2nd ed.). Wiley-Blackwell. ISBN 978-1-4051-0282-7.
^ Paradowski, M. B.; Jelińska, M. (2023). "The predictors of L2 grit and their complex interactions in online foreign language learning: Motivation, self-directed learning, autonomy, curiosity, and language mindsets". Computer Assisted Language Learning: 1–38. doi:10.1080/09588221.2023.2192762.
^ Bassett DS, Sporns O (February 2017). "Network neuroscience". Nature Neuroscience. 20 (3): 353–364. doi:10.1038/nn.4502. PMC 5485642. PMID 28230844.
^ Cite error: The named reference AlexF was invoked but never defined (see the help page).
^ Cite error: The named reference 10.1038/s41598-021-81767-7 was invoked but never defined (see the help page).

[10.3390/en11061381-1] Cite error: The named reference 10.3390/en11061381 was invoked but never defined (see the help page).

[ieeexplore_8191215-2] Cite error: The named reference ieeexplore_8191215 was invoked but never defined (see the help page).

[3] Habibi I, Emamian ES, Abdi A (August 2014). "Quantitative analysis of intracellular communication and signaling errors in signaling networks". BMC Systems Biology. 8: 89. doi:10.1186/s12918-014-0089-z. PMC 4255782. PMID 25115405.

[4] Sindbæk S (2007). Networks and nodal points: the emergence of towns in early Viking Age Scandinavia - Antiquity 81(311). Cambridge University Press. pp. 119–132.

[Paradowskietal2021a-5] Paradowski, M. B.; Jarynowski, A.; Jelińska, M.; Czopek, K. (2021). "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". Language Teaching. 54 (1): 139–143. doi:10.1017/S0261444820000580.

[Paradowskietal2021b-6] Paradowski, M. B.; Jarynowski, A.; Czopek, K.; Jelińska, M.; et al. (2021). "Peer interactions and second language learning: The contributions of Social Network Analysis in Study Abroad vs At-Home environments". In Mitchell, Rosamond; Tyne, Henry (eds.). Language, Mobility and Study Abroad in the Contemporary European Context. New York: Routledge. pp. 99–116. doi:10.1017/S0261444820000580. ISBN 978-10-03087-95-3. S2CID 228863564.

[Paradowskietal2022-7] Paradowski, M. B.; Cierpich-Kozieł, A.; Chen, C.-C.; Ochab, J. K. (2022). "How output outweighs input and interlocutors matter for study-abroad SLA: Computational Social Network Analysis of learner interactions". The Modern Language Journal. 106 (4): 694–725. doi:10.1111/modl.12811. S2CID 255247273.

[8] Harris JK, Luke DA, Zuckerman RB, Shelton SC (June 2009). "Forty years of secondhand smoke research: the gap between discovery and delivery". American Journal of Preventive Medicine. 36 (6): 538–548. doi:10.1016/j.amepre.2009.01.039. OCLC 5899755895. PMID 19372026.

[9] Varda DM, Forgette R, Banks D, Contractor N (2009). "Social Network Methodology in the Study of Disasters: Issues and Insights Prompted by Post-Katrina Research". Population Research and Policy Review. 28 (1): 11–29. doi:10.1007/s11113-008-9110-9. ISSN 0167-5923. OCLC 5659930640. S2CID 144130904.

[10] Sunkersing D, Martin FC, Sullivan P, Bell D (December 2022). "Care and support networks of community-dwelling frail individuals in North West London: a comparison of patient and healthcare workers' perceptions". BMC Geriatrics. 22 (1): 953. doi:10.1186/s12877-022-03561-y. PMC 9737751. PMID 36494627.

[11] Porta D, Diani M (2010). Social Movements 2e: An Introduction (2nd ed.). Wiley-Blackwell. ISBN 978-1-4051-0282-7.

[Paradowski2023-12] Paradowski, M. B.; Jelińska, M. (2023). "The predictors of L2 grit and their complex interactions in online foreign language learning: Motivation, self-directed learning, autonomy, curiosity, and language mindsets". Computer Assisted Language Learning: 1–38. doi:10.1080/09588221.2023.2192762.

[13] Bassett DS, Sporns O (February 2017). "Network neuroscience". Nature Neuroscience. 20 (3): 353–364. doi:10.1038/nn.4502. PMC 5485642. PMID 28230844.

[AlexF-14] Cite error: The named reference AlexF was invoked but never defined (see the help page).

[10.1038/s41598-021-81767-7-15] Cite error: The named reference 10.1038/s41598-021-81767-7 was invoked but never defined (see the help page).

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