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Title: Normalizations in derived networks Authors:  Vladimir Batagelj - IMFM (Slovenia) [presenting]
Abstract: Linked networks are collections of networks over at least two sets and consist of some one-mode networks over single sets and some two-mode networks linking them. 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 $\mathbf{PA}$ describes the authorship relation linking papers $P$ to their authors $A$; and $\mathbf{Ci}$ is a one-mode citation network. Both networks are linked because they share the set of papers $P$. Let $\mathbf{AP}$ denote a network obtained from $\mathbf{PA}$ by reversing directions of all its links. Then the network $\mathbf{AP} * \mathbf{Ci} * \mathbf{PA}$ describes 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. 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 their product fast. Using so called "fractional approach" -- normalizing some matrices in the product we get different weights (with different meaning) in the derived network. We present a theoretical background of normalization in computing derived networks and illustrate the results with analyses of selected bibliographic networks.