====== Layered networks ======
Piran, May 4, 2013
In analysis of citation networks the operation **N**A ⊲ **N**B of layering network **N**A over network **N**B turns out to be useful. Let **N**A = (V,AA,wA) and **N**B = (V,AB) then **N**C = (V,AC,wC) = **N**A ⊲ **N**B, where AC = AA ⋂ AB and (u,v)∈AC ⇒ wC(u,v) = wA(u,v).
Using the layering operation we can define the topics preserving network **CiK** = (**WK** *
**WK**T) ⊲ **Ci**. The weight cikpq = 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
Networks/Cross-Intersection/First
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**T
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 =====
[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-*]
**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.