KQI-based ranking and comparisons.

a, Quadrants of KQI and citation. The scatter diagram shows the triangle at the lower right, which implies that higher citations correspond to higher KQI, but lower citations do not mean lower KQI. Two papers shown in the delta quadrant give examples where valuable literature receives few citations. b, The impact of artificial attacks on rankings. Plot the change curve of KQI and citation rankings by deliberately citing certain articles, adding 1,10,100, or more citations, respectively. The shadow represents the standard deviation of the sample. After the attack, the citation ranking significantly changes more than the KQI ranking. c-e, Citation changes for different hops. By sampling the three shaded areas in a, the number of papers derived from these papers with different hops is shown. It can be observed that articles in region d have a greater aftereffect, while those in region e have a lower aftereffect. f-h, Comparison among h-index, impact factor, PageRank, and KQI [40,41]. The scholars with high citations are more inclined to have higher KQI, while the impact factor of the journal has little relationship with its KQI. KQI and PageRank show a significant positive correlation. i-k, Laureates distribution. The h-index and KQI statistics of Nobel Prize winners (Economics, Physiology & Medicine, Physics, Chemistry) and Turing Award winners show that KQI can better distinguish laureates from ordinary authors (grey). 100% of Nobel Prize winners (Economics) are ranked in the top one-thousandth of KQI, while 51.7% are ranked in the top one-thousandth of h-index. Other results are similar.