Figure 3 | Scientific Reports

Figure 3

From: A Preferential Attachment Paradox: How Preferential Attachment Combines with Growth to Produce Networks with Log-normal In-degree Distributions

Figure 3

(A) Nonlinear tendencies in the attachment rates for various bi-epochally resolved APS citation networks are made apparent on a double logarithmic scale. Four different measurements of \(\hat{A}(k)\) may be distinguished by colour in the plot. Each individual measurement is determined by recording how the publications in time interval T2 = 2000 cite the publications in time intervals T1 = 1990–99 (blue), T1 = 1980–99 (green), T1 = 1970–99 (red), and T1 = 1893–99 (black), respectively. The data have been averaged over a range of k ± 0.025 k. See Table S2 and the surrounding text for details. (B) The attachment rate for the maximally resolved APS citation network is best fit by Redner’s model. Shown is the attachment rate for the maximally resolved APS citation network as calculated by Newman’s measure (black), the estimated log-linear attachment function of Krapivsky’s model (red), and the estimated nonlinear attachment function of Redner’s model (green). The best model (the smallest AIC value) is Redner’s model. Price’s model is not included in the model comparison because it is a special case of Kravipsky’s model. The data have been averaged over a range of k ± 0.025 k.

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