Fig 1.
Schematic cartoon picture of the way science progresses.
(a) Every node represents a paper that makes a significant contribution to science. Red nodes are published past discoveries; grey nodes are yet undiscovered (but discoverable) scientific facts. Black arrows indicate which discovery (or paper) influenced which. The set of dashed green lines is the “adjacent possible”, i.e. the set of scientific facts that can be discovered, given the present state of knowledge (the set of red nodes). Dashed grey lines show novel opportunities that open up once progress has been made. (b) The blow up shows what happens around a significant contribution: many incremental papers (small nodes) repeat, confirm, validate, and explore the “vicinity” of what was found in the breakthrough paper (big red node). These small nodes constitute the mainstream. By definition, incremental papers do not make much headway towards new big discoveries.
Fig 2.
(a) Bibliographic coupling network of the 8673 Physical Review papers published in 1991, PRA purple, PRB turquoise, PRC blue, PRD green, PR Letters red, Reviews of Modern Physics brown. Clusters of all sizes are present. Node size represents the number of citations of these papers in 2011. Clusters are clearly linked by bridging papers. (b) Section of the network, thresholded to link weights two and larger. Node size represents the citation rate during a two-year period after publication, . Many of the immediate citations go to papers close to the cluster centers. (c) Same section for citation rates over a twenty-year period after publication,
. For explicit examples and the meaning of the arrows, see S1 Text. Overall, citation rates over twenty years are smaller than for the first two years. Many papers that are relevant on the long timescale appear in the periphery of clusters (out-of-the-box) and between clusters. Most papers close to cluster centers become marginal on the long timescale. Note the positions of PRL papers (red) and review articles (brown). PRL papers attract much short-term attention but are no longer dominant in the long run. One of the two Rev. Mod. Phys. articles appears in the periphery of a big cluster, the other represents a small emergent field.
Fig 3.
(a) Distribution of the distances of individual papers to the centers of their nearest clusters in the years 1981 (blue), 1991 (red), and 2011 (green). Over time, the distribution shifts toward smaller distances, i.e. more papers tend to appear in cluster centers. (b) The distribution of degrees over the same years shift towards much larger values (tail increases), i.e. there is a tendency to increasingly link to more similar papers. (c) Scatterplot of citations of papers published in 1991, twenty years after their publication, , versus their distance to cluster centers. The 90%, 70%, and 50% quantiles are shown in green, red, and blue, respectively. Citations increase with higher distances from clusters; bridging papers are awarded in the long run. (d) Citations,
, versus their degree. A clear increase is apparent. (e) Distribution of citations for small and large values of distance. The plot is a normalized histogram of the 400 papers with the shortest distances. The blue distribution is for the 400 papers with the largest distance. (f) Distribution of citations for small and large degree.
Fig 4.
(a) Scatterplot of 20-year citations, , versus their PACS entropy, Ii. To control for the strong correlation between Ii and the length of reference list, Li, (ρ = 61), see (b), we show the PACS entropy per reference, Ii/Li, in (c). The effect seen in (a) has vanished and is reversed. Only those 2, 491 papers where enough PACS information is present were considered, see Methods.
Fig 5.
Dependence of citations of authors on network measures; dots now represent authors.
(a) Scatterplot of all citations up to 2011 of all those papers an author has published between 1981 and 1991, versus the average distance of these papers to their respective closest cluster in the BC network in the year of publication. 90%, 70%, and 50% (median) quantiles are shown in green, red, and blue, respectively. Citations increase with higher average distances. (b) Distribution of authors’ citations for short (red) and large (red) distances. The plot is a normalized histogram of the 4000 authors with the smallest distance. The blue distribution is for the 4000 authors with the largest distance. (c) and (d) show the case for the degree. Again, citations increase strongly with degree. The betweenness results are seen in (e) and (f). As for papers, the effect for betweenness is weak.