Linked networks are collections of networks over at least two (sub)sets and consist of some one-mode networks over single subsets and some two-mode networks linking them. For example: the set of nodes consists of two subsets Persons and Organizations. We have two one mode networks describing collaboration between persons and between organizations. A linking two-mode network describes a membership of persons in organizations.
Linked networks were introduced under the name of Meta-matrix approach by Krackhardt in Carley (1998). In current versions of our programs they are not properly supported yet. A very important role in analysis of linked networks plays the network multiplication that enables us to produce so called “derived networks”. For example: a two-mode network PA describes the authorship relation linking papers from P to their authors from A; and Ci is a one-mode citation network. Both networks are linked because they share a common subset of nodes - the set of papers P. Let AP denote a network obtained from PA by reversing the directions of all links in PA. Then the network AP * Ci * PA describes the citations between authors from A. The weight on a link tells us how many times the first author cited in his/her papers the second author.
We presented a theoretical basis of network multiplication and derived networks in our paper Batagelj and Cerinšek (2013). Because large networks are usually sparse (the number of links is of the same order as the number of nodes) it is, in most cases, possible to compute the product of networks fast. We intend to explore which network representations allow for fast network multiplication ant to develop the corresponding algorithms.
Another question related to the network multiplication is the usage of so called “fractional approach”. Some comments on it we presented already in our papers Batagelj, Cerinšek (2013) and Cerinšek, Batagelj (2014), but it seems that there still remain some dilemmas - see recent papers of Perianes-Rodriguez, Waltman, van Eck (2016) and Leydesdorff, Park (2017). We intend to resolve them and build the solutions into our programs. Methodologies developed for analysis of bibliographic linked networks are much more general and can be used on general linked networks.
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