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The index of success of the researchers is now mostly measured using the Hirsch index ($h$). Our recent precise demonstration, that statistically $h \sim \sqrt {N_c} \sim \sqrt {N_p}$, where $N_p$ and $N_c$ denote respectively the total…
The most frequently used indicators for the productivity and impact of scientists are the total number of publication ($N_{pub}$), total number of citations ($N_{cit}$) and the Hirsch (h) index. Since the seminal paper of Hirsch, in 2005,…
The h-index -- the value for which an individual has published at least h papers with at least h citations -- has become a popular metric to assess the citation impact of scientists. As already noted in the original work of Hirsch and as…
Inequalities are abundant in a society with a number of agents competing for a limited amount of resource. Statistics of such social inequalities are usually represented by the Lorenz function $L(p)$, where $p$ fraction of the population…
The Hirsch index or h-index is widely used to quantify the impact of an individual's scientific research output, determining the highest number h of a scientist's papers that received at least h citations. Several variants of the index have…
A number of citation indices have been proposed for measuring and ranking the research publication records of scholars. Some of the best known indices, such as those proposed by Hirsch and Woeginger, are designed to reward most highly those…
The Hirsch index (commonly referred to as h-index) is a bibliometric indicator which is widely recognized as effective for measuring the scientific production of a scholar since it summarizes size and impact of the research output. In a…
We introduce a new centrality index for bipartite network of papers and authors that we call $K$-index. The $K$-index grows with the citation performance of the papers that cite a given researcher and can seen as a measure of scientific…
Prediction of an imminent catastrophic event in a driven disordered system is of paramount importance - from the laboratory scale controlled fracture experiment to the largest scale of mechanical failure i.e., earthquakes. It has been long…
We present a simple generalization of Hirsch's h-index, Z = \sqrt{h^{2}+C}/\sqrt{5}, where C is the total number of citations. Z is aimed at correcting the potentially excessive penalty made by h on a scientist's highly cited papers,…
We analyze the data distributions $f(h)$, $f(N_c$) and $f(N_p)$ of the Hirsch index $(h)$, total citations ($N_c$) and total number of papers ($N_p$) of the top scoring 120,000 authors (scientists) from the Stanford cite-score (or c-score)…
Citation distributions are lognormal. We use 30 lognormally distributed synthetic series of numbers that simulate real series of citations to investigate the consistency of the h index. Using the lognormal cumulative distribution function,…
Hirsch has introduced the h-index to quantify an individual's scientific research output by the largest number h of a scientist's papers that received at least h citations. In order to take into account the highly skewed frequency…
The h index was introduced by Hirsch to quantify an individual's scientific research output. It has been widely used in different fields to show the relevance of the research work of prominent scientists. I have worked out 26 practical…
We study the inequality of citations received for different publications of various researchers and Nobel laureates in Physics, Chemistry, Medicine and Economics using Google Scholar data from 2012 to 2024. Citation distributions are found…
The $K$-index is an easily computable centrality index in complex networks, such as a scientific citations network. A researcher has a $K$-index equal to $K$ if he or she is cited by $K$ articles that have at least $K$ citations. The…
In order to advance academic research, it is important to assess and evaluate the academic influence of researchers and the findings they produce. Citation metrics are universally used methods to evaluate researchers. Amongst the several…
The impact of individual scientists is commonly quantified using citation-based measures. The most common such measure is the h-index. A scientist's h-index affects hiring, promotion, and funding decisions, and thus shapes the progress of…
The h-index was introduced by the physicist J.E. Hirsch in 2005 as measure of a researcher's productivity. We consider the "combinatorial Fermi problem" of estimating h given the citation count. Using the Euler-Gauss identity for integer…
J. E. Hirsch (2005) introduced the h-index to quantify an individual's scientific research output by the largest number h of a scientist's papers, that received at least h citations. This so-called Hirsch index can be easily modified to…