Agent-based model for the h-index – exact solution

Abstract

Hirsch’s h-index is perhaps the most popular citation-basedmeasure of scientific excellence. In 2013, Ionescu and Chopard proposed an agent-basedmodel describing a process for generating publications and citations in an abstractscientific community [G. Ionescu, B. Chopard, Eur. Phys. J. B 86, 426(2013)]. Within such a framework, one may simulate a scientist’s activity, and – byextension – investigate the whole community of researchers. Even though the Ionescu andChopard model predicts the h-index quite well, the authors provided a solutionbased solely on simulations. In this paper, we complete their results with exact, analyticformulas. What is more, by considering a simplified version of the Ionescu-Chopard model,we obtained a compact, easy to compute formula for the h-index. The derivedapproximate and exact solutions are investigated on a simulated and real-world datasets.