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=== Preparing a citation network ===
It is necessary to prepare a [[citation network]] before starting main path analysis. In a citation network, the nodes arerepresent the documents such as academic articles, patents, or legal cases. These nodes a connected using citation information. Citation networks are by nature directed. They are directed because the two nodes associatedon the opposite end withof a link is not symmetrical in their roles. As regards to the direction, this article adopts the convention that the cited node points to the citing node, signifying the fact that knowledge in the cited node flows to the citing node. Citation network are also by nature acyclic, which means that a node can never chain back to itself followingif theone directedmoves link.along Severalthe termslinks relatedfollowing totheir citationdirection. network are defined here before proceeding further .
HeadsSeveral andterms tails:related to citation network are defined here before proceeding further. Heads are the nodes the direction arrow leads to. Tails are the nodes on other end of the direction arrow. Sources are the nodes that are cited, but cite no others. Sinks cite other nodes, but are not cited. Ancestors are the nodes that can be traced back to from a target node. Descendants are the nodes that one can reach from a target if one moves along the links following their direction .
Sources and sinks: Sources are the nodes that are cited, but cite no others. Sinks cite other nodes, but are not cited.
Ancestors and descendants: Ancestors are the nodes that can be traced back to. Descendants are the nodes that one can reach following the links.
=== Traversal counts ===
=== Path search ===
Based on the traversal counts, one can then search for the most significant path(s). There are several ways of finding them, including local search, global, and key-route search.
==== Local search ====
ThisLocal issearch mentioned in Hummon and Doreian<ref name=":0" /> as "priority first" search. In the search process, local search chooses the next link with the highest SPX as the outgoing link. It keeps tracking the most traversed link thus obtainobtains the main stream among all citation chains.
==== Global search ====
Global search simply suggest the pathcitation chain with the largest overall SPX. The concept of global search is similar to [[critical path method]] in project scheduling.
==== Key-route search ====
Key-route search is designed to avoid the problem of missing significant links in both the local and global search. As described in Liu and Lu (2012)<ref name=":1" />, the approach searches main paths from the specified links (key-routes) thus guarantees the inclusion of the links. inOne thecan specify multiple links to obtain multiple main paths. OtherOne notable advantage of the key-route approach is that by varying the number of key-routes one is able to obtaincontrol the detail of the main paths inby differentvarying detailsthe number of key-routes. The larger the number of key-route is specified, the more detail is givenreveals. When the number of key-route increases to a certain point the search returns the whole citation network.
== The Variants ==
In addition to the key-route search approach, variations of the method include approachesthe approach that areis aggregative and stochastic<ref>{{Cite journal|last=Yeo|first=Woondong|last2=Kim|first2=Seonho|last3=Lee|first3=Jae-Min|last4=Kang|first4=Jaewoo|date=2014-01-01|title=Aggregative and stochastic model of main path identification: a case study on graphene|url=https://link.springer.com/article/10.1007/s11192-013-1140-3|journal=Scientometrics|language=en|volume=98|issue=1|pages=633–655|doi=10.1007/s11192-013-1140-3|issn=0138-9130}}</ref>, considerconsiders decay in knowledge diffusion<ref>{{Cite journal|last=Liu|first=John S.|last2=Kuan|first2=Chung-Huei|date=2016-02-01|title=A new approach for main path analysis: Decay in knowledge diffusion|url=http://onlinelibrary.wiley.com/doi/10.1002/asi.23384/abstract|journal=Journal of the Association for Information Science and Technology|language=en|volume=67|issue=2|pages=465–476|doi=10.1002/asi.23384|issn=2330-1643}}</ref>, etc.
== Applications ==
The method has been applied to three types of documenting system that hasmaintain the tradition of making references to the previous documents. They are the academic article, patent, and judicial documentdocumenting system.
=== Academic article ===
Academic citation databases such as [[Web of Science]] and [[Scopus]] includesinclude comprehensive digitized citation information. thusThese information make it possible to apply main path analysis to examine the knowledge structure or trace the knowledge flow of any scientific fields. Some early worksapplications explores on the subject of centrality-productivity<ref>{{Cite journal|last=Hummon|first=Norman P.|last2=Doreian|first2=Patrick|last3=Freeman|first3=Linton C.|date=2016-08-18|title=Analyzing the Structure of the Centrality-Productivity Literature Created Between 1948 and 1979|url=http://journals.sagepub.com/doi/10.1177/107554709001100405|journal=Knowledge|language=en|volume=11|issue=4|pages=459–480|doi=10.1177/107554709001100405}}</ref>, conflict resolution<ref>{{Cite journal|last=Carley|first=Kathleen M.|last2=Hummon|first2=Norman P.|last3=Harty|first3=Martha|date=2016-08-17|title=Scientific Influence|url=https://doi.org/10.1177/107554709301400406|journal=Knowledge|language=en|volume=14|issue=4|pages=417–447|doi=10.1177/107554709301400406}}</ref>, etc. More recent investigations on scientific fieldsapplications includesinclude fullerenes<ref name=":3" />, nanotubes<ref name=":3" />, data envelopment analysis<ref name=":2" /><ref>{{Cite journal|last=Liu|first=John S.|last2=Lu|first2=Louis Y.Y.|last3=Lu|first3=Wen-Min|title=Research fronts in data envelopment analysis|url=https://doi.org/10.1016/j.omega.2015.04.004|journal=Omega|volume=58|pages=33–45|doi=10.1016/j.omega.2015.04.004}}</ref><ref>{{Cite journal|last=Liu|first=John S.|last2=Lu|first2=Louis Y.Y.|last3=Lu|first3=Wen-Min|last4=Lin|first4=Bruce J.Y.|title=A survey of DEA applications|url=https://doi.org/10.1016/j.omega.2012.11.004|journal=Omega|volume=41|issue=5|pages=893–902|doi=10.1016/j.omega.2012.11.004}}</ref>, supply chain management<ref>{{Cite journal|last=Claudia Colicchia|last2=Fernanda Strozzi|date=2012-06-15|title=Supply chain risk management: a new methodology for a systematic literature review|url=http://www.emeraldinsight.com/doi/abs/10.1108/13598541211246558|journal=Supply Chain Management: An International Journal|volume=17|issue=4|pages=403–418|doi=10.1108/13598541211246558|issn=1359-8546}}</ref>, corporate social responsibility<ref>{{Cite journal|last=Lu|first=Louis Y.Y.|last2=Liu|first2=John S.|date=2014-03-01|title=The Knowledge Diffusion Paths of Corporate Social Responsibility – From 1970 to 2011|url=http://onlinelibrary.wiley.com/doi/10.1002/csr.1309/abstract|journal=Corporate Social Responsibility and Environmental Management|language=en|volume=21|issue=2|pages=113–128|doi=10.1002/csr.1309|issn=1535-3966}}</ref>, IT outsourcing<ref>{{Cite journal|last=Liang|first=Huigang|last2=Wang|first2=Jian-Jun|last3=Xue|first3=Yajiong|last4=Cui|first4=Xiaocong|title=IT outsourcing research from 1992 to 2013: A literature review based on main path analysis|url=http://dx.doi.org/10.1016/j.im.2015.10.001|journal=Information & Management|volume=53|issue=2|pages=227–251|doi=10.1016/j.im.2015.10.001}}</ref>, medical tourism<ref>{{Cite journal|last=Chuang|first=Thomas C.|last2=Liu|first2=John S.|last3=Lu|first3=Louis Y.Y.|last4=Lee|first4=Yachi|title=The main paths of medical tourism: From transplantation to beautification|url=https://doi.org/10.1016/j.tourman.2014.03.016|journal=Tourism Management|volume=45|pages=49–58|doi=10.1016/j.tourman.2014.03.016}}</ref>, etc.
=== Patent ===
Patents referencing prior arts is also a common practice. For example, each United States patent document includes a "References Cited" section that lists the prior arts of the patent. Patent databasedatabases such as [[Clarivate Analytics]], and Webpat, provide containdigitized patent citation information. Verspagen (2007)<ref>{{Cite journal|last=Verspagen|first=Bart|date=2007-03-01|title=Mapping technological trajectories as patent citation networks: a study on the history of fuel cell research|url=http://www.worldscientific.com/doi/abs/10.1142/S0219525907000945|journal=Advances in Complex Systems|volume=10|issue=01|pages=93–115|doi=10.1142/S0219525907000945|issn=0219-5259}}</ref> and Mina (2007)<ref>{{Cite journal|last=Mina|first=A.|last2=Ramlogan|first2=R.|last3=Tampubolon|first3=G.|last4=Metcalfe|first4=J.S.|title=Mapping evolutionary trajectories: Applications to the growth and transformation of medical knowledge|url=https://doi.org/10.1016/j.respol.2006.12.007|journal=Research Policy|volume=36|issue=5|pages=789–806|doi=10.1016/j.respol.2006.12.007}}</ref> are the two early works that apply main path analysis to the patent data.
=== Judicial document ===
In the common law system, a court decision document usually references previously published opinions for the purpose of justifying the current decision. These judicial references, or legal citations, can also be used to construct citation network.networks Theand opportunities forthen tracing the changechanges of legal opinions. Research opportunity usingin thesethis informationarea areis wide open. Liu et al. (2014)<ref name=":4" /> haveconducted aan exploratory trystudy on such application.
== Software Implementation ==
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