# Differences

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notes:net:layer [2015/07/16 21:27] (current)
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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>
+[run biblio macro normal]
+Network/2-mode/Transpose 2-mode
+[select transposed as Second]
+[select normalized as First]
+Networks/Multiply Networks
+[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.