# Layered networks

Piran, May 4, 2013

In analysis of citation networks the operation NANB of layering network NA over network NB turns out to be useful. Let NA = (V,AA,wA) and NB = (V,AB) then NC = (V,AC,wC) = NANB, 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 * WKT) ⊲ 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 * WKT 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
[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.