Abstract
We discuss microscopic mechanisms of complex network growth, with the special emphasis of how these mechanisms can be evaluated from the measurements on real networks. As an example we consider the network of citations to scientific papers. Contrary to common belief that its growth is determined by the linear preferential attachment, our microscopic measurements show that it is driven by the nonlinear autocatalytic growth. This invalidates the scale-free hypothesis for the citation network. The nonlinearity is responsible for a dramatic dynamical phase transition: while the citation lifetime of majority of papers is 6–10 years, the highly-cited papers have practically infinite lifetime.
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Notes
Consider a cohort of papers published in the same year. After a couple of years, when the general interest to this cohort already decayed, the annual number of citations gained by previously uncited papers is either 0 or 1. Therefore, the mean annual number of additional citations gained by previously uncited papers is \(\overline{\Delta k_{i}}\approx\Delta N_{0}/N_{0}\) where N 0 is the number of uncited papers and ΔN 0=N 0(t)−N 0(t+1) is the number of uncited papers that got their first citation during recent year t+1. If the total number of papers in the dataset is N, then \(\overline{\Delta k_{i}}\approx\Delta P_{0}/P_{0}\) where P 0=N 0/N is the fraction of uncited papers.
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Acknowledgements
We are grateful to Filippo Radicchi, Alexander Petersen, Oleg Yordanov, and Andrea Scharnhorst for fruitful discussions.
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Golosovsky, M., Solomon, S. The Transition Towards Immortality: Non-linear Autocatalytic Growth of Citations to Scientific Papers. J Stat Phys 151, 340–354 (2013). https://doi.org/10.1007/s10955-013-0714-z
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DOI: https://doi.org/10.1007/s10955-013-0714-z