Figure 4

Ranking journals and sub-fields by lack of knowledge flows. The analysis of missing links restricted to specific sub-fields of physics or single APS journals confirms that the tendency of a citation to occur between a pair of articles increases with the similarity between the bibliographies of the two articles. Panels (a)-(b) show the plots of \(U(p^{*}) = 1 - P_{i\to j}(p^{*})\) for different sub-graphs corresponding to (a) two families of PACS codes, namely 40 (electromagnetism) and 50 (Gases and Plasmas), and (b) two APS journals, namely Physical Review Letters and Physical Review C. In panel (c) we sketch the procedure adopted to compute the estimate \(\widetilde{U}_{0}\): we consider the line tangent to the curve \(U(p^{*})\) at the smallest value of the statistical threshold \(p^{*}\) for which we still have a relatively substantial number of validated pairs (in this case, \(p^{*}=10^{-7}\)), and we define \(\widetilde{U}_{0}\) as the value of the intercept at \(p^{*}=0\) of that line. In panels (d) and (e) we show, respectively, the rankings of sub-fields and APS journals based on the values of \(\widetilde{U}_{0}\). Notice that Electromagnetism and Interdisciplinary physics are the two sub-fields with the smallest percentage of missing links, i.e., those in which knowledge among articles flows effectively and as would be expected if citations were driven by overlaps between topics or research problems. Interestingly, the lack of knowledge flows between articles published in Physical Review C (\(\widetilde{U}_{0}\simeq 0.27\)) is almost nine times as large as the one identified in Physical Review Letters (\(\widetilde{U}_{0}\simeq0.03\)), which is the APS journal with the widest visibility and largest impact.