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{{Short description|Mathematical tool}}

Main path analysis was first proposed by Hummon and Doreian<ref name=":0">{{Cite journal|last=Hummon|first=Norman P.|last2=Doreian|first2=Patrick|date=|title=Connectivity in a citation network: The development of DNA theory|url=https://doi.org/10.1016/0378-8733(89)90017-8|journal=Social Networks|volume=11|issue=1|pages=39–63|doi=10.1016/0378-8733(89)90017-8|via=}}</ref>. It is a mathematical tool to identify the major paths in a [[directed acyclic graph]] (DAG), typically [[citation network]]. The method begins by measuring the significance of all the links in a citation network through the concept of ‘traversal count’ and then sequentially chains the most significant links into a ‘main path’, which is deemed the most significant historical path in the target DAG. The method is applicable to any human activity that can be organized in the form of a DAG. The most common applications are tracing the knowledge flow paths or development trajectories of a science or technology field through bibliographic citations or patent citations<ref name=":2">{{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=Data envelopment analysis 1978–2010: A citation-based literature survey|url=https://doi.org/10.1016/j.omega.2010.12.006|journal=Omega|volume=41|issue=1|pages=3–15|doi=10.1016/j.omega.2010.12.006}}</ref><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><ref name=":3">{{Cite journal|last=Lucio-Arias|first=Diana|last2=Leydesdorff|first2=Loet|date=2008-10-01|title=Main-path analysis and path-dependent transitions in HistCite™-based historiograms|url=http://onlinelibrary.wiley.com/doi/10.1002/asi.20903/abstract|journal=Journal of the American Society for Information Science and Technology|language=en|volume=59|issue=12|pages=1948–1962|doi=10.1002/asi.20903|issn=1532-2890}}</ref>. It has also been applied to judicial decision to trace the evolving changes of legal opinion<ref>{{Cite journal|last=Liu|first=John S.|last2=Chen|first2=Hsiao-Hui|last3=Ho|first3=Mei Hsiu-Ching|last4=Li|first4=Yu-Chen|date=2014-12-01|title=Citations with different levels of relevancy: Tracing the main paths of legal opinions|url=http://onlinelibrary.wiley.com/doi/10.1002/asi.23135/abstract|journal=Journal of the Association for Information Science and Technology|language=en|volume=65|issue=12|pages=2479–2488|doi=10.1002/asi.23135|issn=2330-1643}}</ref>.

'''Main path analysis''' is a mathematical tool, first proposed by [[Norman P. Hummon|Hummon]] and [[Patrick Doreian|Doreian]] in 1989,<ref name=":0">{{Cite journal|last1=Hummon|first1=Norman P.|last2=Doreian|first2=Patrick|year=1989|title=Connectivity in a citation network: The development of DNA theory|journal=Social Networks|volume=11|issue=1|pages=39–63|doi=10.1016/0378-8733(89)90017-8}}</ref> to identify the major paths in a [[citation network]], which is one form of a [[directed acyclic graph]] (DAG). It has since become an effective technique for mapping technological trajectories, exploring scientific knowledge flows, and conducting literature reviews. [[File:Global key-route main paths for a citation network.svg|thumb|Main path analysis uncovers the most significant paths, or citation chains, in a citation network. The figure shows the global key-route main paths (in red) for a sample citation network (based on search path count and at key-route 1).|220x220px]]

Main path analysis was first proposed by Hummon and Doreian<ref name=":0">{{Cite journal|last=Hummon|first=Norman P.|last2=Doreian|first2=Patrick|date=|title=Connectivity in a citation network: The development of DNA theory|url=https://doi.org/10.1016/0378-8733(89)90017-8|journal=Social Networks|volume=11|issue=1|pages=39–63|doi=10.1016/0378-8733(89)90017-8|via=}}</ref>. It is a mathematical tool to identify the major paths in a [[directed acyclic graph]] (DAG), typically [[citation network]]. The method begins by measuring the significance of all the links in a citation network through the concept of ‘traversal count’ and then sequentially chains the most significant links into a ‘main"main path’path", which is deemed the most significant historical path in the target DAG[[citation network]]. The method is applicable to any human activity that can be organized in the form of a DAG[[citation network]]. The mostmethod commonis applicationscommonly areapplied tracingto trace the knowledge flow paths or development trajectories of a science or technology field, through bibliographic citations or patent citations.<ref name=":2">{{Cite journal|lastlast1=Liu|firstfirst1=John S.|last2=Lu|first2=Louis Y.Y.|last3=Lu|first3=Wen-Min|last4=Lin|first4=Bruce J.Y.|title=Data envelopment analysis 1978–2010: A citation-based literature survey|url=https://doi.org/10.1016/j.omega.2010.12.006|journal=Omega|volume=41|issue=1|pages=3–15|doi=10.1016/j.omega.2010.12.006|year=2013}}</ref><ref name="Verspagen 93–115">{{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=011|pages=93–115|doi=10.1142/S0219525907000945|issn=0219-5259|url=http://collections.unu.edu/view/UNU:1191}}</ref><ref name=":3">{{Cite journal|lastlast1=Lucio-Arias|firstfirst1=Diana|last2=Leydesdorff|first2=Loet|date=2008-10-01|title=Main-path analysis and path-dependent transitions in HistCite™-based historiograms|url=http://onlinelibrary.wiley.com/doi/10.1002/asi.20903/abstract|journal=Journal of the American Society for Information Science and Technology|language=en|volume=59|issue=12|pages=1948–1962|doi=10.1002/asi.20903|issn=1532-2890}}</ref>. It has also been applied to judicial decisiondecisions to trace the evolving changes of legal opinionopinions.<ref name=":4">{{Cite journal|lastlast1=Liu|firstfirst1=John S.|last2=Chen|first2=Hsiao-Hui|last3=Ho|first3=Mei Hsiu-Ching|last4=Li|first4=Yu-Chen|date=2014-12-01|title=Citations with different levels of relevancy: Tracing the main paths of legal opinions|url=http://onlinelibrary.wiley.com/doi/10.1002/asi.23135/abstract|journal=Journal of the Association for Information Science and Technology|language=en|volume=65|issue=12|pages=2479–2488|doi=10.1002/asi.23135|issn=2330-1643}}</ref> Main path analysis has attracted scholars attention recently. Academic research related to main path analysis saw a fast growing since 2007. A list of academic articles that introduce, explain, apply, modify, or extend the method originated in Hummon and Doreian<ref name=":0" /> can be found [https://davincierlab.weebly.com/list-of-main-path-articles.html here]. Nevertheless, there are issues not broadly discussed in applying the method, including the handling of citation data, choosing a proper traversal weight scheme, search options, and interpretation of the resulting paths.<ref>{{Cite journal|last1=Liu|first1=John S.|last2=Lu|first2=Louis Y. Y.|last3=Ho|first3=Mei Hsiu-Ching|date=2019-04-01|title=A few notes on main path analysis|journal=Scientometrics|language=en|volume=119|issue=1|pages=379–391|doi=10.1007/s11192-019-03034-x|issn=1588-2861|doi-access=free}}</ref>

== History ==

Main path analysis is first propoedproposed in Hummon and Doreian (1989)<ref name=":0" /> in which they suggest a different approach for analyzing a citation network "where the connective threads through a network are preserved and the focus is on the links in the network rather than on the nodes."<ref name=":0" /> They call the resulting chain of the most used citation links "main path" and claim that "It is our intuition that the main path, selected on the basis of the most used path will identify the main stream of a literature." The idea was verified using a set of DNA research articles. To make the method more practical, Liu and Lu (2012)<ref name=":1">{{Cite journal|lastlast1=Liu|firstfirst1=John S.|last2=Lu|first2=Louis Y.Y.|date=2012-03-01|title=An integrated approach for main path analysis: Development of the Hirsch index as an example|url=http://onlinelibrary.wiley.com/doi/10.1002/asi.21692/abstract|journal=Journal of the American Society for Information Science and Technology|language=en|volume=63|issue=3|pages=528–542|doi=10.1002/asi.21692|issn=1532-2890}}</ref> proposedextends the method to include the key-route search. The most useful feature of the key-route search is that one is able to view the different level of main paths by adjusting the key-route numbers.

== The method ==

Main path analysis  operates in two steps. The first step obtains the traversal countcounts of each link in a DAGcitation network. Several algorithmstypes of traversal counts are mentioned in the literature to calculate traversal count. The second step searches for the main paths by linking the significant links according to the size of traversal counts. Hereafter,One theneeds methodto isprepare explaineda assumingcitation thenetwork thebefore DAGproceeding isfor amain citationpath networkanalysis.

=== 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 aare connected using citation information. Citation networks are by nature directed. They are directed because the two nodes associatedon withthe opposite end of a link isare 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 areis also by nature acyclic, which means that a node can never chain back to itself followingif theone directedmoves link.along Severalthe termslinks relatedfollowing to citation network are defined here before proceeding furthertheir direction.

HeadsSeveral andterms tails:related to a citation network are defined here before proceeding further. Heads are the nodes the direction arrow leads to. Tails are the nodes on other endends 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.

[[File:SPC values for a citation network.png|thumb|Figure 1. SPC values for a sample citation network]]

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 ===

Traversal counts measuresmeasure the significance of a link. LiteratureThe literature discusses several types of traversal counts, including search path count (SPC), search path link count (SPLC), search path node pair (SPNP), and other variations.<ref name=":5" /> All these traversal counts will be noted as SPX.

[[File:SPLC values for a citation network.png|thumb|Figure 2. SPLC values for a sample citation network]]

==== Search path count (SPC) ====

A link’s SPC is the number of times the link is traversed if one runs through all possible paths from all the sources to all the sinks. SPC is first proposed by [[Vladimir Batagelj]].<ref>Batagelj, V. (2003). Efficient algorithms for citation network analysis. &nbsp;''arXiv preprint cs/0309023''.</ref> SPC values for each link in a sample citation network is shown in Figure 1. The SPC value for the link (B, D) is 5 because five paths (B-D-F-H-K, B-D-F-I-L, B-D-F-I-M-N, B-D-I-L, and B-D-I-M-N) traverse through it.

[[File:SPNP values for a citation network.png|thumb|Figure 3. SPNP values for a sample citation network]]

==== Search path nodelink paircount (SPNPSPLC) ====

A link’s SPC is the number of times the link is traversed if one runs through all possible paths from all the sources to all the sinks. SPC is first proposed by Vladimir Batagelj<ref>Batagelj, V. (2003). Efficient algorithms for citation network analysis. ''arXiv preprint cs/0309023''.</ref>.

A link’s SPLC is the number of times the link is traversed if one runs through all possible paths from all the ancestors of the tail node (including itself) to all the sinks.  SPLC is first proposed by Hummon and Doreian.<ref name=":0" /> Figure 2 presents the SPLC values for each link in the same citation network as shown in Figure 1. Six paths traverse through the link (D, F) thus give it the SPLC value 6. They are: B-D-F-H-K, B-D-F-I-L, B-D-F-I-M-N, D-F-H-K, D-F-I-L, and D-F-I-M-N, noting that all the paths begin either from the ancestor of D, which is B, and D itself.

==== Search path linknode countpair (SPLCSPNP) ====

A link’s SPNP is the number of times the link is traversed if one runs through all possible paths from all the ancestors of the tail node (including itself) to all the descendants of the head node (including itself). SPNP is first proposed by Hummon and Doreian.<ref name=":0" /> The SPNP values of the link (C, H) is 6 because there are 6 paths that begin from A, B, C (A and B are C's ancestors) and end at H and K (K is H's descendant). These paths are A-C-H, A-C-H-K, B-C-H, B-C-H-K, C-H, and C-H-K.

[[File:Local main paths SPC.png|thumb|Figure 4. Local main paths in a sample citation network]]

A link’s SPLC is the number of times the link is traversed if one runs through all possible paths from all the ancestors of the tail node (including itself) to all the sinks. SPLC is first proposed by Hummon and Doreian<ref name=":0" />.

Search path node pair (SPNP)

A link’s SPNP is the number of times the link is traversed if one runs through all possible paths from all the ancestors of the tail node (including itself) to all the descendants of the head node (including itself). SPNP is first proposed by Hummon and Doreian<ref name=":0" />.

=== 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.

[[File:Global main paths SPC.png|thumb|Figure 5. Global main paths in a sample citation network]]

==== Local search ====

ThisLocal search is mentioned in Hummon and Doreian<ref name=":0" /> as "priority first" search. In theThis search process, local searchalways chooses the next link(s) with the highest SPX as the outgoing link. It keeps tracking the most traversed link(s) thus obtainobtains the main stream among all citation chains. Figure 4 shows the local main paths that are obtained based on SPC. Noticing that when the search reaches the node I, two outgoing links have the same SPC values thus producing two paths afterward.

[[File:Local key-route main paths SPC.png|thumb|Figure 6. Local key-route main paths in a sample citation network]]

==== Global search ====

Global search simply suggestsuggests the pathcitation chain with the largest overall SPX. The concept of global search is similar to the [[critical path method]] in project scheduling. The global main paths of the sample citation network based on SPC is presented in Figure 5. The sum of all the SPC values in the path B-D-F-I-M-N is 15, which is the largest among all possible paths.

[[File:Global key-route main paths SPC.png|thumb|Figure 7. Global key-route main paths in a sample citation network]]

==== Key-route search ====

Key-route search is designed to avoid the problem of missing significant links in both the local and global search. The problem is in the local and global main paths shown above, in which one of the most important links (H, K) is not included in the main paths. 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 also specify multiple links to obtain multiple main paths. OtherAn notableadditional advantage of the key-route approach is that by varyingone theis numberable ofto key-routescontrol onethe isdetail ableof to obtainthe main paths inby differentvarying detailsthe number of key-routes. The larger the number of key-route is specified, the more detail is givenrevealed. When the number of key-route increases to a certain point the search returns the whole citation network. Figure 6 and 7 show the local key-route and global key-route main paths of the sample citation network. In both main paths the number of key-route is set to 1, i.e., doing the search base on only the top links. Since there are two top links (B, D) and (H, K), the resulting main paths include both of them.

== 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|lastlast1=Yeo|firstfirst1=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 name=":5">{{Cite journal|lastlast1=Liu|firstfirst1=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 legaljudicial casedocumenting 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|lastlast1=Hummon|firstfirst1=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|lastlast1=Carley|firstfirst1=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|lastlast1=Liu|firstfirst1=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|year=2016}}</ref><ref>{{Cite journal|lastlast1=Liu|firstfirst1=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|year=2013}}</ref>, supply chain management,<ref>{{Cite journal|lastlast1=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|lastlast1=Lu|firstfirst1=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|lastlast1=Liang|firstfirst1=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|year=2016}}</ref>, medical tourism,<ref>{{Cite journal|lastlast1=Chuang|firstfirst1=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|year=2014}}</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|lastname="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|lastlast1=Mina|firstfirst1=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|year=2007}}</ref> are the two early works that apply main path analysis to the patent data.

=== LegalJudicial casedocument ===

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 networks and then tracing the changes of legal opinions. Research opportunity in this area is wide open. Liu et al. (2014)<ref name=":4" /> conducted an exploratory study on such type of application.

== Software Implementation ==

Main path analysis is implemented in [http://mrvar.fdv.uni-lj.si/pajek/ Pajek], a widely used freeware[[social network analysis]] software written by [[Vladimir Batagelj]] and Andrej Mrvar of [[University of Ljubljana]], Slovenia. To run main path analysis in Pajek, one needs to first prepare a citation network and have Pajek reads in the network. Next, in the Pajek main menu, computes the traversal counts of all links in the network applying one of the following command sequences (depending on the choice of traversal counts).

''<small>Network → Acyclic Network → Create Weighted Network + Vector → Traversal Weights → Search Path Link Count (SPC), or</small>''

Line 68 ⟶ 72:

After traversal counts are computed, the following command sequences find the main paths.

For local main paths 

''<small>Network → Acyclic Network → Create (Sub)Network → Main Paths → Local Search → Forward</small>''

Line 83 ⟶ 87:

''<small>Network → Acyclic Network → Create (Sub)Network → Main Paths → Global Search → Key-Route</small>''

In addition to key-route search, a more flexible search feature is added starting from Pajek version 5.03 (January 4, 2018). The new feature allows for local and global search passing through vertices defined by a cluster. The command sequences are as follows:

''<small>Network → Acyclic Network → Create (Sub)Network → Main Paths → Local Search → Key-Route → Through Vertices in Cluster</small>''

''<small>Network → Acyclic Network → Create (Sub)Network → Main Paths → Global Search → Key-Route → Through Vertices in Cluster</small>''

== References ==

Line 88 ⟶ 98:

== External links ==

* [http://mrvar.fdv.uni-lj.si/pajek/ Pajek], a free social network analysis software.

* [https://davincierlab.weebly.com/list-of-main-path-articles.html List of main path articles], this page contain a list of academic articles that introduce, explain, apply, modify, or extend the method originated in Hummon and Doreian.

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[[Category:Social networks]]