[[notes:net:layer]]

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,A_{A},w_{A}) and **N**_{B} = (V,A_{B}) then **N**_{C} = (V,A_{C},w_{C}) = **N**_{A} ⊲ **N**_{B}, where A_{C} = A_{A} ⋂ A_{B} and (u,v)∈A_{C} ⇒ w_{C}(u,v) = w_{A}(u,v).

Using the layering operation we can define the topics preserving network **CiK** = (**WK** *
**WK**^{T}) ⊲ **Ci**. The weight cik_{pq} = 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.

[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.

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