Network theory

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For the theory regarding the regulation of the adaptive immune system, see Immune network theory. For the sociological theory, see Social network.
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In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes 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

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.

Network optimization

Network problems that involve finding an optimal way of doing something are studied as

critical path analysis, and program evaluation and review technique
.

Network analysis

Electric network analysis

The analysis of electric power systems could be conducted using network theory from two main points of view:

  1. 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.[1]
  2. Weighted graphs that blend an abstract understanding of complex network theories and electric power systems properties.[2]

Social network analysis

web sites, or scholarly publications
.

Since the 1970s, the empirical study of networks has played a central role in social science, and many of the

exchange relationships and of social mechanisms in setting prices.[21] It has been used to study recruitment into political movements, armed groups, and other social organizations.[22] It has also been used to conceptualize scientific disagreements[23] as well as academic prestige.[24] More recently, network analysis (and its close cousin traffic analysis) has gained a significant use in military intelligence,[25] for uncovering insurgent networks of both hierarchical and leaderless nature.[citation needed
]

Biological network analysis

See also: Metabolic network, proteome, metabolome, and omics

With the recent explosion of publicly available high throughput biological data, the analysis of molecular networks has gained significant interest.[26] 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 motifs are small subgraphs that are over-represented in the network. Similarly, 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 networks with respect to diseases has led to the development of the field of network medicine.[27] Recent examples of application of network theory in biology include applications to understanding the cell cycle[28] as well as a quantitative framework for developmental processes.[29]

Narrative network analysis

Narrative network of US Elections 2012[30]

The automatic parsing of textual corpora has enabled the extraction of actors and their relational networks on a vast scale. The resulting narrative networks, 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.[31] This automates the approach introduced by Quantitative Narrative Analysis,[32] whereby subject-verb-object triplets are identified with pairs of actors linked by an action, or pairs formed by actor-object.[30]

Link analysis

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.[33][34]

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.[35]

Centrality measures

Information about the relative importance of nodes and edges in a graph can be obtained through

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[36]
of a node is the most relevant centrality measure.

Assortative and disassortative mixing

Further information: 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.[37]

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.[38][39][40]

Spatial networks

Many real networks are embedded in space. Examples include, transportation and other infrastructure networks, brain neural networks. Several models for spatial networks have been developed.[41]

Spread

Content in a

infectious diseases
, neural excitation, information and rumors, etc.

Network immunization

The question of how to immunize efficiently scale free networks which represent realistic networks such as the Internet and social networks has been studied extensively. One such strategy is to immunize the largest degree nodes, i.e., targeted (intentional) attacks[43] since for this case is relatively high and fewer nodes are needed to be immunized. However, in most realistic networks the global structure is not available and the largest degree nodes are unknown.

See also

References

  1. ^
    PMID 24710095
    .
  2. ^
    S2CID 44685630
    . Retrieved 2018-06-07.
  3. 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.
  5. doi:10.1017/S0261444820000580
    .
  6. S2CID 228863564
    .
  7. S2CID 255247273
    .
  8. PMID 19372026
    .
  9. S2CID 144130904
    .
  10. PMID 36494627
    .
  11. ISBN 978-1-4051-0282-7
    .
  12. doi:10.1080/09588221.2023.2192762
    .
  13. PMID 28230844
    .
  14. ^ Alex Fornito. "An Introduction to Network Neuroscience: How to build, model, and analyse connectomes - 0800-10:00 | OHBM". pathlms.com. Retrieved 2020-03-11.
  15. PMID 33500525
    .
  16. doi:10.3166/lcn.10.3.37-54
    . Retrieved 2014-10-15.
  17. MIT
    Press, 2012.
  18. ^ Newman, M.E.J. Networks: An Introduction. Oxford University Press. 2010
  19. PMC 7123536
    .
  20. PMID 17222078
    .
  21. S2CID 158776581
    .
  22. doi:10.1146/annurev-polisci-041719-102523
    .
  23. PMID 29795624
    .
  24. S2CID 143724478
    . Retrieved 22 September 2021.
  25. ^ Roberts N, Everton SF. "Strategies for Combating Dark Networks" (PDF). Journal of Social Structure. 12. Retrieved 22 September 2021.
  26. PMID 25290670
    .
  27. PMID 21164525
    .
  28. PMID 21865350
    .
  29. PMID 29021161
    .
  30. ^ a b Automated analysis of the US presidential elections using Big Data and network analysis; S Sudhahar, GA Veltri, N Cristianini; Big Data & Society 2 (1), 1–28, 2015
  31. ^ Network analysis of narrative content in large corpora; S Sudhahar, G De Fazio, R Franzosi, N Cristianini; Natural Language Engineering, 1–32, 2013
  32. ^ Quantitative Narrative Analysis; Roberto Franzosi; Emory University © 2010
  33. ISSN 0003-0007
    .
  34. S2CID 3032237
    .
  35. ^ Attardi G, Di Marco S, Salvi D (1998). "Categorization by Context" (PDF). Journal of Universal Computer Science. 4 (9): 719–736.
  36. S2CID 18365246
    .
  37. S2CID
    15186389.
  38. S2CID 7761398
    .
  39. S2CID 18979395
    .
  40. S2CID 119118006
    .
  41. doi:10.1109/49.12889
    .
  42. ^ Newman M, Barabási AL, Watts DJ, eds. (2006). The Structure and Dynamics of Networks. Princeton, N.J.: Princeton University Press.
  43. S2CID 2325768
    .

Books

External links

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