Editing Network theory (section)

== Network analysis ==

=== Electric network analysis ===
The analysis of electric power systems could be conducted using network theory from two main points of view:
# An abstract perspective (i.e., as a graph consists from nodes and edges), regardless of the electric power aspects (e.g., transmission line impedances). Most of these studies focus only on the abstract structure of the power grid using node degree distribution and betweenness distribution, which introduces substantial insight regarding the vulnerability assessment of the grid. Through these types of studies, the category of the grid structure could be identified from the complex network perspective (e.g., single-scale, scale-free). This classification might help the electric power system engineers in the planning stage or while upgrading the infrastructure (e.g., add a new transmission line) to maintain a proper redundancy level in the transmission system.<ref name="10.3390/en11061381"/>
# Weighted graphs that blend an abstract understanding of complex network theories and electric power systems properties.<ref name="ieeexplore_8191215"/>

===Social network analysis===
[[File:Social Network Analysis Visualization.png|thumb|right|Visualization of social network analysis<ref>{{Cite journal | volume = 10| issue = 3| vauthors = Grandjean M | title = La connaissance est un réseau| journal =Les Cahiers du Numérique| access-date = 2014-10-15| date = 2014| pages = 37–54| url = http://www.cairn.info/resume.php?ID_ARTICLE=LCN_103_0037| doi=10.3166/lcn.10.3.37-54}}</ref>]]'''[[Social network analysis]]''' examines the structure of relationships between social entities.<ref>[[Wasserman, Stanley]] and Katherine Faust. 1994. ''Social Network Analysis: Methods and Applications.'' Cambridge: Cambridge University Press. Rainie, Lee and [[Barry Wellman]], ''Networked: The New Social Operating System.'' Cambridge, MA: [[MIT]] Press, 2012.
</ref> These entities are often persons, but may also be [[Group (sociology)|groups]], [[organizations]], [[nation states]], [[web sites]], or [[scientometrics|scholarly publications]].

Since the 1970s, the empirical study of networks has played a central role in social science, and many of the [[Mathematics|mathematical]] and [[Statistics|statistical]] tools used for studying networks have been first developed in [[sociology]].<ref name="Newman">Newman, M.E.J. ''Networks: An Introduction.'' Oxford University Press. 2010</ref>  Amongst many other applications, social network analysis has been used to understand the [[diffusion of innovations]], news and rumors.<ref name="Al-Taie">{{cite book | vauthors = Al-Taie MZ, Kadry S |chapter=Information Diffusion in Social Networks |title=Python for Graph and Network Analysis |series=Advanced Information and Knowledge Processing |date=2017 |pages=165–184  |doi=10.1007/978-3-319-53004-8_8 |pmc=7123536 |isbn=978-3-319-53003-1 }}</ref>  Similarly, it has been used to examine the spread of both [[epidemiology|diseases]] and [[Medical sociology|health-related behaviors]].<ref name="Luke">{{cite journal | vauthors = Luke DA, Harris JK | title = Network analysis in public health: history, methods, and applications | journal = Annual Review of Public Health | volume = 28 | issue = 1 | pages = 69–93 | date = April 2007 | pmid = 17222078 | doi = 10.1146/annurev.publhealth.28.021406.144132 | doi-access = free }}</ref>  It has also been applied to the [[Economic sociology|study of markets]], where it has been used to examine the role of trust in [[Social exchange|exchange relationships]] and of social mechanisms in setting prices.<ref name="Odabaş">{{cite journal | vauthors = Odabaş M, Holt TJ, Breiger RL |title=Markets as Governance Environments for Organizations at the Edge of Illegality: Insights From Social Network Analysis |journal=American Behavioral Scientist |date=October 2017 |volume=61 |issue=11 |pages=1267–1288 |doi=10.1177/0002764217734266 |hdl=10150/631238 |s2cid=158776581 |hdl-access=free }}</ref>  It has been used to study recruitment into [[political movement]]s, armed groups, and other social organizations.<ref name="Larson">{{cite journal | vauthors = Larson JM |title=Networks of Conflict and Cooperation |journal=Annual Review of Political Science |date=11 May 2021 |volume=24 |issue=1 |pages=89–107 |doi=10.1146/annurev-polisci-041719-102523 |doi-access=free }}</ref>   It has also been used to conceptualize scientific disagreements<ref name="Leng">{{cite journal | vauthors = Leng RI | title = A network analysis of the propagation of evidence regarding the effectiveness of fat-controlled diets in the secondary prevention of coronary heart disease (CHD): Selective citation in reviews | journal = PLOS ONE | volume = 13 | issue = 5 | pages = e0197716 | date = 24 May 2018 | pmid = 29795624 | pmc = 5968408 | doi = 10.1371/journal.pone.0197716 | doi-access = free | bibcode = 2018PLoSO..1397716L }}</ref> as well as academic prestige.<ref name="Burris">{{cite journal | vauthors = Burris V |title=The Academic Caste System: Prestige Hierarchies in PhD Exchange Networks |journal=American Sociological Review |date=April 2004 |volume=69 |issue=2 |pages=239–264 |doi=10.1177/000312240406900205 |s2cid=143724478 |url=https://journals.sagepub.com/doi/10.1177/000312240406900205 |access-date=22 September 2021|url-access=subscription }}</ref>  More recently, network analysis (and its close cousin [[traffic analysis]]) has gained a significant use in military intelligence,<ref name="Roberts">{{cite journal | vauthors = Roberts N, Everton SF |title= Strategies for Combating Dark Networks |journal=Journal of Social Structure |volume=12 |url=https://www.cmu.edu/joss/content/articles/volume12/RobertsEverton.pdf |access-date=22 September 2021}}</ref> for uncovering insurgent networks of both hierarchical and [[leaderless resistance|leaderless]] nature.{{citation needed|date=July 2015}}

===Biological network analysis===
{{see also|Metabolic network|proteome|metabolome|omics}}
With the recent explosion of publicly available high throughput [[biological data]], the analysis of molecular networks has gained significant interest.<ref>{{cite journal | vauthors = Habibi I, Emamian ES, Abdi A | title = Advanced fault diagnosis methods in molecular networks | journal = PLOS ONE | volume = 9 | issue = 10 | pages = e108830 | date = 2014-10-07 | pmid = 25290670 | pmc = 4188586 | doi = 10.1371/journal.pone.0108830 | doi-access = free | bibcode = 2014PLoSO...9j8830H }}</ref> The type of analysis in this context is closely related to social network analysis, but often focusing on local patterns in the network. For example, [[network motif]]s are small subgraphs that are over-represented in the network. Similarly, [[Network motif#Activity motifs|activity motifs]] are patterns in the attributes of nodes and edges in the network that are over-represented given the network structure. Using networks to analyze patterns in biological systems, such as food-webs, allows us to visualize the nature and strength of interactions between species. The analysis of [[biological network]]s with respect to diseases has led to the development of the field of [[network medicine]].<ref>{{cite journal | vauthors = Barabási AL, Gulbahce N, Loscalzo J | title = Network medicine: a network-based approach to human disease | journal = Nature Reviews. Genetics | volume = 12 | issue = 1 | pages = 56–68 | date = January 2011 | pmid = 21164525 | pmc = 3140052 | doi = 10.1038/nrg2918 }}</ref>  Recent examples of application of network theory in biology include applications to understanding the [[cell cycle]]<ref>{{cite journal | vauthors = Jailkhani N, Ravichandran S, Hegde SR, Siddiqui Z, Mande SC, Rao KV | title = Delineation of key regulatory elements identifies points of vulnerability in the mitogen-activated signaling network | journal = Genome Research | volume = 21 | issue = 12 | pages = 2067–2081 | date = December 2011 | pmid = 21865350 | pmc = 3227097 | doi = 10.1101/gr.116145.110 }}</ref> as well as a quantitative framework for developmental processes.<ref>{{cite journal | vauthors = Jackson MD, Duran-Nebreda S, Bassel GW | title = Network-based approaches to quantify multicellular development | journal = Journal of the Royal Society, Interface | volume = 14 | issue = 135 | pages = 20170484 | date = October 2017 | pmid = 29021161 | pmc = 5665831 | doi = 10.1098/rsif.2017.0484 }}</ref>

=== Narrative network analysis ===
[[File:Tripletsnew2012.png|thumb|right|Narrative network of US Elections 2012<ref name="Reference">{{Cite journal |last1=Sudhahar |first1=Saatviga |last2=Veltri |first2=Giuseppe A |last3=Cristianini |first3=Nello |date=2015 |title=Automated analysis of the US presidential elections using Big Data and network analysis |url=http://journals.sagepub.com/doi/10.1177/2053951715572916 |journal=Big Data & Society |language=en |volume=2 |issue=1 |pages=205395171557291 |doi=10.1177/2053951715572916|hdl=2381/31767 |hdl-access=free }}</ref>]]
The automatic parsing of ''[[Text corpus|textual corpora]]'' has enabled the extraction of actors and their relational networks on a vast scale. The resulting [[narrative network]]s, which can contain thousands of nodes, are then analyzed by using tools from Network theory to identify the key actors, the key communities or parties, and general properties such as robustness or structural stability of the overall network, or centrality of certain nodes.<ref>[http://orcp.hustoj.com/wp-content/uploads/2016/01/2013-Network-analysis-of-narrative-content-in-large-corpora.pdf Network analysis of narrative content in large corpora]; S Sudhahar, G De Fazio, R Franzosi, N Cristianini; Natural Language Engineering, 1–32, 2013</ref> This automates the approach introduced by Quantitative Narrative Analysis,<ref>Quantitative Narrative Analysis; Roberto Franzosi; Emory University © 2010</ref> whereby subject-verb-object triplets are identified with pairs of actors linked by an action, or pairs formed by actor-object.<ref name="Reference" />

===Link analysis===
[[Link analysis]] is a subset of network analysis, exploring associations between objects. An example may be examining the addresses of suspects and victims, the telephone numbers they have dialed, and financial transactions that they have partaken in during a given timeframe, and the familial relationships between these subjects as a part of police investigation. Link analysis here provides the crucial relationships and associations between very many objects of different types that are not apparent from isolated pieces of information. Computer-assisted or fully automatic computer-based link analysis is increasingly employed by [[bank]]s and [[insurance]] agencies in [[fraud]] detection, by telecommunication operators in telecommunication network analysis, by medical sector in [[epidemiology]] and [[pharmacology]], in law enforcement [[Criminal procedure|investigation]]s, by [[search engine]]s for [[relevance]] rating (and conversely by the [[search engine spammer|spammers]] for [[spamdexing]] and by business owners for [[search engine optimization]]), and everywhere else where relationships between many objects have to be analyzed. Links are  also derived from similarity of time behavior in both nodes. Examples include climate networks where the links between two locations (nodes) are determined, for example, by the similarity of the rainfall or temperature fluctuations in both sites.<ref name="TsonisSwanson2006">{{cite journal| vauthors = Tsonis AA, Swanson KL, Roebber PJ |title=What Do Networks Have to Do with Climate?|journal=Bulletin of the American Meteorological Society|volume=87|issue=5|year=2006|pages=585–595|issn=0003-0007|doi=10.1175/BAMS-87-5-585|bibcode=2006BAMS...87..585T|doi-access=free}}</ref><ref name="Boers2014">{{cite journal | vauthors = Boers N, Bookhagen B, Barbosa HM, Marwan N, Kurths J, Marengo JA | title = Prediction of extreme floods in the eastern Central Andes based on a complex networks approach | journal = Nature Communications | volume = 5 | pages = 5199 | date = October 2014 | pmid = 25310906 | doi = 10.1038/ncomms6199 | s2cid = 3032237 | doi-access = free | bibcode = 2014NatCo...5.5199B | author5-link = Jürgen Kurths }}</ref>

====Web link analysis====
Several [[Web search]] [[ranking]] algorithms use link-based centrality metrics, including [[Google]]'s [[PageRank]], Kleinberg's [[HITS algorithm]], the [[CheiRank]] and [[TrustRank]] algorithms. Link analysis is also conducted in information science and communication science in order to understand and extract information from the structure of collections of web pages. For example, the analysis might be of the interlinking between politicians' websites or blogs. Another use is for classifying pages according to their mention in other pages.<ref>{{cite journal| vauthors = Attardi G, Di Marco S, Salvi D |title=Categorization by Context|journal=[[Journal of Universal Computer Science]]|year=1998|volume=4|issue=9|pages=719–736|url=http://www.jucs.org/jucs_4_9/categorisation_by_context/Attardi_G.pdf}}</ref>

===Centrality measures===
Information about the relative importance of nodes and edges in a graph can be obtained through [[centrality]] measures, widely used in disciplines like [[sociology]]. For example, [[eigenvector centrality]] uses the [[eigenvectors]] of the [[adjacency matrix]] corresponding to a network, to determine nodes that tend to be frequently visited. Formally established measures of centrality are [[degree centrality]], [[closeness centrality]], [[betweenness centrality]], [[eigenvector centrality]], [[subgraph centrality]], and [[Katz centrality]]. The purpose or objective of analysis generally determines the type of centrality measure to be used. For example, if one is interested in dynamics on networks or the robustness of a network to node/link removal, often the [[dynamical importance]]<ref>{{cite journal | vauthors = Restrepo JG, Ott E, Hunt BR | title = Characterizing the dynamical importance of network nodes and links | journal = Physical Review Letters | volume = 97 | issue = 9 | pages = 094102 | date = September 2006 | pmid = 17026366 | doi = 10.1103/PhysRevLett.97.094102 | arxiv = cond-mat/0606122 | s2cid = 18365246 | bibcode = 2006PhRvL..97i4102R }}</ref>  of a node is the most relevant centrality measure.

===Assortative and disassortative mixing===
{{see|Assortative mixing}}
These concepts are used to characterize the linking preferences of hubs in a network. Hubs are nodes which have a large number of links. Some hubs tend to link to other hubs while others avoid connecting to hubs and prefer to connect to nodes with low connectivity. We say a hub is assortative when it tends to connect to other hubs. A disassortative hub avoids connecting to other hubs. If hubs have connections with the expected random probabilities, they are said to be neutral. There are three methods to quantify degree correlations.<ref>M. E. J. Newman (2003). "Mixing patterns in networks". ''Physical Review E''. '''67''' (2): 026126. [[ArXiv (identifier)|arXiv]]:cond-mat/0209450. [[Bibcode (identifier)|Bibcode]]:2003PhRvE..67b6126N. [[Doi (identifier)|doi]]:10.1103/PhysRevE.67.026126. [[PMID (identifier)|PMID]] 12636767. [[S2CID (identifier)|S2CID]] 15186389.</ref>

===Recurrence networks===
The recurrence matrix of a [[recurrence plot]] can be considered as the adjacency matrix of an undirected and unweighted network. This allows for the analysis of time series by network measures. Applications range from detection of regime changes over characterizing dynamics to synchronization analysis.<ref name="marwan2009">{{cite journal| vauthors = Marwan N, Donges JF, Zou Y, Donner RV, Kurths J |title=Complex network approach for recurrence analysis of time series|journal=Physics Letters A|volume=373|issue=46|year=2009|pages=4246–4254|issn=0375-9601|doi=10.1016/j.physleta.2009.09.042|arxiv=0907.3368|bibcode=2009PhLA..373.4246M|s2cid=7761398}}</ref><ref name="donner2011">{{cite journal| vauthors = Donner RV, Heitzig J, Donges JF, Zou Y, Marwan N, Kurths J |title=The Geometry of Chaotic Dynamics – A Complex Network Perspective|journal=European Physical Journal B|volume=84|issue=4|year=2011|pages=653–672|issn=1434-6036|doi=10.1140/epjb/e2011-10899-1|arxiv=1102.1853|bibcode=2011EPJB...84..653D|s2cid=18979395}}</ref><ref name="feldhoff2013">{{cite journal| vauthors = Feldhoff JH, Donner RV, Donges JF, Marwan N, Kurths J |title=Geometric signature of complex synchronisation scenarios|journal=Europhysics Letters |volume=102 |issue=3 |year=2013|pages=30007|issn=1286-4854|doi=10.1209/0295-5075/102/30007|arxiv=1301.0806|bibcode=2013EL....10230007F|s2cid=119118006}}</ref>