Abstract
We analyze the citation time-series of manuscripts in three different fields of science; physics, social science and technology. The evolution of the time-series of the yearly number of citations, namely the citation trajectories, diffuse anomalously, their variance scales with time ∝t 2H , where H ≠ 1/2. We provide detailed analysis of the various factors that lead to the anomalous behavior: non-stationarity, long-ranged correlations and a fat-tailed increment distribution. The papers exhibit a high degree of heterogeneity across the various fields, as the statistics of the highest cited papers is fundamentally different from that of the lower ones. The citation data is shown to be highly correlated and non-stationary; as all the papers except the small percentage of them with high number of citations, die out in time.
Highlights
Studying the structure of underlying patterns in different fields of science gives insight into the evolutionary process of the system over time, and provides the ability to make general assumptions about its future [1–3]
We provide detailed analysis of the various factors that lead to the anomalous behavior: non-stationarity, long-ranged correlations and a fat-tailed increment distribution
We study the yearly citation time series in three different fields: physics, social science and technology
Summary
Studying the structure of underlying patterns in different fields of science gives insight into the evolutionary process of the system over time, and provides the ability to make general assumptions about its future [1–3]. We use two different methods to calculate the temporal behavior of the average yearly number of citations, as well as their variance, and we study the non-stationarity of the time series, its correlations and the effect of large fluctuations. In sub-Sec. II B, we investigate the mean and variance of the yearly citation number, comparing time- and ensemble-averages, for all the papers in the field, as well as when we separate between different classes depending on their total number of citations after 34 years. II B, we investigate the mean and variance of the yearly citation number, comparing time- and ensemble-averages, for all the papers in the field, as well as when we separate between different classes depending on their total number of citations after 34 years
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