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Several terms 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 .
[[File:SPC values for a citation network.png|thumb|Figure 1. SPC values for a sample citation network]]
=== Traversal counts ===
Traversal counts measures the significance of a link. 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. ''arXiv preprint cs/0309023''.</ref>. SPC values for each link in a sample citation network is show in Figure 1. The SPC value for link (B,D) is 5 because five paths (B-D-F-H-K, B-D-F-I-L, B-D-I-L, B-D-I-M-M, and B-J-M-N) travese through it.
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Search path link count (SPLC)
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. 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-K, D-F-H-K, D-F-I-L, and D-F-I-M-K, noting that the paths begin from the ancestor of D, which is B, and itself.
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" />. The SPNP values of (C,H) is 6 because there are 6 paths that are begin from A, B (they are C's ancestors) and C, and end at H and K (H's descendant). These paths are: A-C-H-K
[[File:Local main paths SPC.png|thumb|Figure 4. Local main paths in a sample citation network]]
=== 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, global, and key-route search.
[[File:Global main paths SPC.png|thumb|Figure 5. Global main paths in a sample citation network]]
==== Local search ====
Local search 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 obtains the main stream among all citation chains.
[[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 suggest the citation chain with the largest overall SPX. The concept of global search is similar to [[critical path method]] in project scheduling.
[[File:Global key-route main paths SPC.png|thumb|Figure 6. Global key-route main paths in a sample citation network]]
==== Key-route search ====
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== The Variants ==
In addition to the key-route search approach, variations of the method include the approach that is 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>, considers decay in knowledge diffusion<ref name=":5">{{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 ==
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