Seite - (000254) - in Knowledge and Networks

250 subsequent papers, and the same distribution of these citations over time (Fig. 12.3, left panel and middle panel). The right panel of Fig. 12.3 showed the distributions of observed frequency and expected frequency of journal papers for the example paper above. Specifically, we used a variation of the Markov Chain Monte Carlo (MCMC) algorithm to construct randomized citation networks for all papers in the WOS data- base. The switching of endpoints of citation links was constrained to randomly cho- sen endpoints within the same class (Fig. 12.3), where the link classes are defined as having the same origin year and target year (Itzkovitz et al., 2003). One can think of each link class as a sub-graph of the global citation network, which can then be randomized in the usual way by performing Q*E switches, where E is the number of links in the subgraph. There is no proof for when the Markov Chain converges; however, it is suggested (Itzkovitz et al., 2003) to set Q at a safe value of 100. Since the citation network has 302 million edges, the scale of the computation is large, and we used a slightly less conservative value of Q = 2log(E) to reduce computational burden. As can be noted in the original paper on the MCMC switching algorithm (Itzkovitz et al., 2003), this value of Q is well within the region where correlations with the original network cannot be detected. 30 25 15 5 10 0 0 2 4 6 8 10 100 101 102 103 104 105 20 Years after publication Yearly Cumulative Before switch After switch 2002 2001 2000 A B C 2002 2001 2000 A′ B′ C 1.00 0.80 0.60 0.40 0.20 0.00 Frequency Observed Expected Fig. 12.3 Link switching in the null model and example distributions of observed and expected frequency of journal pairs. Citation links between papers are switched randomly but constrained to have the same origin year and target year. Thus in the left panel, switching links A and B are allowed, while switching links A and C are not allowed. The switching algorithm thus preserves for each paper its (i) number of references, (ii) citation count, (iii) citation accumulation dynamics, and (iv) the age distribution of referenced work. Performing QE switches converges to a random graph from the configuration model (Itzkovitz et al., 2003) where the number of and dynamics of citations are preserved, but the origin of the citations is randomized. Since each node is equally likely to be the originating node of any citation, given the constraints, we know a priori that no disciplines exist in this randomized citation network. The middle panel above demonstrates the citation history of a paper. The citation history of every paper is exactly preserved under our null model, ensuring that we control for both the variation in magnitude and dynamics of citation accu- mulation to papers. The right panel above further shows, for the example paper highlighted in Table 12.1, the frequency distribution for the observed journal pairings (blue line) and the fre- quency distribution for these journal pairings when averaged across instances of the null model (red line). From Uzzi et al. (2013b, p. 12). Copyright 2013 by Science. Reprinted with permission from the authors and Science S. Mukherjee et al.