The transition towards immortality: non-linear autocatalytic growth of citations to scientific papers

TL;DR

This paper reveals that citation networks grow through nonlinear autocatalytic mechanisms rather than linear preferential attachment, leading to a phase transition where highly-cited papers have near-infinite lifetimes.

Contribution

It provides microscopic measurements demonstrating nonlinear growth in citation networks, challenging the scale-free hypothesis and explaining the long-term impact of highly-cited papers.

Findings

Citation growth is driven by nonlinear autocatalytic mechanisms.

The network exhibits a dynamical phase transition.

Highly-cited papers have effectively infinite citation lifetime.

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.