[[notes:net:layer]]

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+ | ====== Layered networks ====== | ||

+ | Piran, May 4, 2013 | ||

+ | |||

+ | In analysis of citation networks the operation **N**<sub>A</sub> ⊲ **N**<sub>B</sub> of layering network **N**<sub>A</sub> over network **N**<sub>B</sub> turns out to be useful. Let **N**<sub>A</sub> = (V,A<sub>A</sub>,w<sub>A</sub>) and **N**<sub>B</sub> = (V,A<sub>B</sub>) then **N**<sub>C</sub> = (V,A<sub>C</sub>,w<sub>C</sub>) = **N**<sub>A</sub> ⊲ **N**<sub>B</sub>, where A<sub>C</sub> = A<sub>A</sub> ⋂ A<sub>B</sub> and (u,v)∈A<sub>C</sub> ⇒ w<sub>C</sub>(u,v) = w<sub>A</sub>(u,v). | ||

+ | |||

+ | Using the layering operation we can define the topics preserving network **CiK** = (**WK** * | ||

+ | **WK**<sup>T</sup>) ⊲ **Ci**. The weight cik<sub>pq</sub> = number of keywords common to the citing work p and cited work q. | ||

+ | |||

+ | Andrej told me, that the layering operation can be done in Pajek using | ||

+ | <code> | ||

+ | Networks/Cross-Intersection/First | ||

+ | </code> | ||

+ | I tried to determine the **CiK** network in JoC (Journal of Classification) network data: |W| = 81581, |A| = 37690, |K| = 21509, |Des| = 4188. The product **WK** * **WK**<sup>T</sup> | ||

+ | was computed in some seconds, but it took almost half an hour for layering. The efficiency could be improved reducing first networks to works with a complete description. | ||

+ | |||

+ | The result was relatively small network on 3569 nodes. I got 36 link islands of size [5,80]. The weights were quite large - papers with long abstracts. It is necessary to apply the normalization. | ||

+ | |||

+ | ===== Normalized topics preserving network ===== | ||

+ | |||

+ | <code> | ||

+ | [read WK] | ||

+ | [run biblio macro normal] | ||

+ | Network/2-mode/Transpose 2-mode | ||

+ | [select transposed as Second] | ||

+ | [select normalized as First] | ||

+ | Networks/Multiply Networks | ||

+ | [read Cite] | ||

+ | [select Cite as Second] | ||

+ | [select product as First] | ||

+ | Networks/Cross-Intersection/First | ||

+ | Network/Create Partition/Degree/All | ||

+ | Operations/Network+Partition/Extract Subnetwork [1-*] | ||

+ | </code> | ||

+ | **To do:** Restrict first to works with complete description and make macro. | ||

+ | |||

+ | **To do:** Output the list of keywords for links in a given island. | ||

+ | |||

+ | **To do:** For a given island output the changes in common keywords. |

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