Figure 4

Overview of the measured attachment rates for growing network representations of the APS journal collection data at daily, monthly, and yearly time resolutions. (A) The attachment rates plotted in isolation. Each \({\hat{A}}_{k}\) was estimated using Newman’s measure from APS journal publications dating from July 1893 through 2003 inclusive. The data have been averaged over a range of k ± 0.025 k. (B) The same attachment rates fitted using the segmented linear regression technique discussed in the main text. A larger linearity score reflects a stronger log-linear tendency in a measured attachment rate. The yearly attachment rate is the most log-linear by this score. (C) The attachment rates are fitted by 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 in the case of daily and monthly time resolution, but Krapivsky’s model in the case of yearly time resolution. Price’s model is not included in the model comparison because it is a special case of Kravipsky’s model.