The π<Subscript>v</Subscript>-index: a new indicator to characterize the impact of journals

For determining the eminence of scientific journals, a new indicator stressing the importance of papers in the “elite set” (i.e., highly cited papers) is suggested. The number of papers in the elite set (P _πv) is calculated with the equation: (10 log P) − 10, where P is the total number of papers in the set. The one-hundredth of citations (C) obtained by P _πv papers is regarded as the π_v-index which is field and time dependent. The π_v-index is closely correlated with the citedness (C/P) of P _πv papers, and it is also correlated with the Hirsch-index. Three types of Hirsch-sets are distinguished, depending on the relation of the number of citations received by the Hirsch-paper (ranked as h) and the paper next in rank (h + 1) by citation. The h-index of an Anomalous Hirsch-set (AH) may be increased by a single citation to a paper outside the Hirsch-core. (A set of papers may be regarded as AH, where the number of citations to the Hirsch-paper is higher than the h-index and the next paper in rank shows as many citations as the value of the h-index.)     

Beyond the Durfee square: Enhancing the h-index to score total publication output

An individual’s h-index corresponds to the number h of his/her papers that each has at least h citations. When the citation count of an article exceeds h, however, as is the case for the hundreds or even thousands of citations that accompany the most highly cited papers, no additional credit is given (these citations falling outside the so-called “Durfee square”). We propose a new bibliometric index, the “tapered h-index” (h _T), that positively enumerates all citations, yet scoring them on an equitable basis with h. The career progression of h _T and h are compared for six eminent scientists in contrasting fields. Calculated h _T for year 2006 ranged between 44.32 and 72.03, with a corresponding range in h of 26 to 44. We argue that the h _T-index is superior to h, both theoretically (it scores all citations), and because it shows smooth increases from year to year as compared with the irregular jumps seen in h. Conversely, the original h-index has the benefit of being conceptually easy to visualise. Qualitatively, the two indices show remarkable similarity (they are closely correlated), such that either can be applied with confidence. Sadly, after a long and distinguished career, Peter Killworth died on 28 Jan 2008.     

Tailor based allocations for multiple authorship: a fractional gh-index

A quantitative modification to keep the number of published papers invariant under multiple authorship is suggested. In those cases, fractional allocations are attributed to each co-author with a summation equal to one. These allocations are tailored on the basis of each author contribution. It is denoted “Tailor Based Allocations (TBA)” for multiple authorship. Several protocols to TBA are suggested. The choice of a specific TBA may vary from one discipline to another. In addition, TBA is applied to the number of citations of a multiple author paper to have also this number conserved. Each author gets only a specific fraction of the total number of citations according to its fractional paper allocation. The equivalent of the h-index obtained by using TBA is denoted the gh-index. It yields values which differ drastically from those given by the h-index. The gh-index departs also from [`(h)]\bar{h} recently proposed by Hirsh to account for multiple authorship. Contrary to the h-index, the gh-index is a function of the total number of citations of each paper. A highly cited paper allows a better allocation for all co-authors while a less cited paper contributes essentially to one or two of the co-authors. The scheme produces a substantial redistribution of the ranking of scientists in terms of quantitative records. A few illustrations are provided.     

Fairly sharing the credit of multi-authored papers and its application in the modification of <Emphasis Type="Italic">h</Emphasis>-index and <Emphasis Type="Italic">g</Emphasis>-index

Except the alphabetic ordering authorship papers, the citations of multi-authored papers are allocated to the authors based on their contributions to the paper. For papers without clarification of contribution proportion, a function of author number and rank is presented to rightly determine the credit allocated proportion and allocated citations of each author. Our citation allocation scheme is between the equally fractional counting and the one using the inverse of author rank. It has a parameter to adjust the credit distribution among the different authors. The allocated citations can either be used alone to indicate one’s performance in a paper, or can be applied in the modification of h-index and g-index to represent the achievement of a scientist on the whole. The modified h-index and g-index of an author makes use of more papers in which he or she played important roles. Our method is suitable for the papers with wide range of author numbers.     

The h-index of h-index and of other informetric topics

In this paper we examine the applicability of the concept of h-index to topics, where a topic has index h, if there are h publications that received at least h citations and the rest of the publications on the topic received at most h citations. We discuss methodological issues related to the computation of h-index of topics (denoted h-b index by BANKS [2006]). Data collection for computing the h-b index is much more complex than computing the index for authors, research groups and/or journals, and has several limitations. We demonstrate the methods on a number of informetric topics, among them the h-index.     

h-index sequence and h-index matrix: Constructions and applications

Summary The calculation of Hirsch's h-index is a detail-ignoring way, therefore, single h-index could not reflect the difference of time spans for scientists to accumulate their papers and citations. In this study the h-index sequence and the h-index matrix are constructed, which complement the absent details of single h-index, reveal different increasing manner and the increasing mechanism of the h-index, and make the scientists at different scientific age comparable.     

The size and impact of the elite set of publications in scientometric assessments

Several scientometric impact indicators [total citations, h, g, and π-index, percentage rank position (PRP), weighted citation share (WCS)] of 190 elite papers of 15 members of the Hungarian Academy of Sciences active in three different fields were calculated. From the indices the PRP indicator proved to be independent of the citation practices in the fields. The PRP index of a journal paper can be calculated in per cent as unity minus (the rank number of the paper by citation frequency within the publishing journal minus one divided with the total number of papers in the journal) times hundred. The sum of the PRP index of the elite papers of a scientist may characterize his or her total publication performance. The size of the elite set of journal papers within the total was calculated by different methods. The h-index and g-index corresponds to the size of the elite, i.e. number of the elite papers according to the h-statistics and g-statistics, respectively. The number of papers in the π-set is equal to the square root of total papers. The π-index equals to one hundredth of citations to the π-set papers. In the present paper the size of the elite set is determined as the number of papers in the h-set, g-set, or π-set, and as 10 % of total papers, or number of papers cited 2, 3, or 5 times the mean citation rate (MCR) of the publishing journal. The π-citation threshold model is presented for demonstrating how MCR and the distribution of citations over the papers may influence the size of the elite set and the corresponding π-index. It was found that the scientific performances concluded from the π-index obtained from elite sets of different size are in good agreement.     

Rational (successive) <Emphasis Type="Italic">h</Emphasis>-indices: An application to economics in the Republic of Ireland

We rank economics departments in the Republic of Ireland according to the number of publications, number of citations, and successive h-index of research-active staff. We increase the discriminatory power of the h ₁-index by introducing three generalizations, each of which is a rational number. The first (h ₁ ⁺) measures the excess over the actual h-index, while the other two (h ₁*, h ₁ ^Δ) measures the distance to the next h-index. At the individual level, h* and h ^Δ coincide while h ⁺ is undefined.     

Applying the <Emphasis Type="Italic">h</Emphasis>-index in exploring bibliometric properties of elite marketing scholars

The h-index is a recent metric that captures a scholar’s influence. In the current work, it is used to: (1) obtain the h-index scores of the most productive scholars in the Journal of Consumer Research (JCR), and compare these to other elite scholars (including those of the other three premier marketing journals); (2) demonstrate the relationship between the h-indices and total number of citations of the top JCR producers; (3) examine the h-indices of Ferber winners (best interdisciplinary paper based on a doctoral dissertation published in JCR in a given year) and those having received honorable mentions; (4) explore the relationship between a marketing journal’s prestige and the corresponding h-index score of its editor. These varied analyses demonstrate the multitudinous ways in which the h-index can be used when investigating bibliometric phenomena within a given discipline.     

Does the <Emphasis Type="Italic">h</Emphasis>-index for ranking of scientists really work?

Summary Hirsch (2005) has proposed the h-index as a single-number criterion to evaluate the scientific output of a researcher (Ball, 2005): A scientist has index h if h of his/her N_p papers have at least h citations each, and the other (N_p − h) papers have fewer than h citations each. In a study on committee peer review (Bornmann & Daniel, 2005) we found that on average the h-index for successful applicants for post-doctoral research fellowships was consistently higher than for non-successful applicants.     

Probing the <Emphasis Type="Italic">h</Emphasis>-core: an investigation of the tail–core ratio for rank distributions

The set of citations received by a set of publications consists of citations received by articles in the h-core and citations received by articles in the h-tail. Denoting the cardinalities of these fours sets as C, P, C _H and C _T we introduce the tail-core ratio (C _T/C _H) and show that in practical cases this ratio tends to increase. Introducing further the k-index, defined as k = (C/P)/(C _T/C _H), we show that this index decreases in most practical cases. A power law model is in accordance with these practical observations.     

Analysis of bibliometric indicators for individual scholars in a large data set

Citation numbers and other quantities derived from bibliographic databases are becoming standard tools for the assessment of productivity and impact of research activities. Though widely used, still their statistical properties have not been well established so far. This is especially true in the case of bibliometric indicators aimed at the evaluation of individual scholars, because large-scale data sets are typically difficult to be retrieved. Here, we take advantage of a recently introduced large bibliographic data set, Google Scholar Citations, which collects the entire publication record of individual scholars. We analyze the scientific profile of more than 30,000 researchers, and study the relation between the h-index, the number of publications and the number of citations of individual scientists. While the number of publications of a scientist has a rather weak relation with his/her h-index, we find that the h-index of a scientist is strongly correlated with the number of citations that she/he has received so that the number of citations can be effectively be used as a proxy of the h-index. Allowing for the h-index to depend on both the number of citations and the number of publications, we find only a minor improvement.     

Weighted indices for evaluating the quality of research with multiple authorship

Devising an index to measure the quality of research is a challenging task. In this paper, we propose a set of indices to evaluate the quality of research produced by an author. Our indices utilize a policy that assigns the weights to multiple authors of a paper. We have considered two weight assignment policies: positionally weighted and equally weighted. We propose two classes of weighted indices: weighted h-indices and weighted citation h-cuts. Further, we compare our weighted h-indices with the original h-index for a selected set of authors. As opposed to h-index, our weighted h-indices take into account the weighted contributions of individual authors in multi-authored papers, and may serve as an improvement over h-index. The other class of weighted indices that we call weighted citation h-cuts take into account the number of citations that are in excess of those required to compute the index, and may serve as a supplement to h-index or its variants.     

The H l -index: improvement of H-index based on quality of citing papers

This paper proposes h _l -index as an improvement of the h-index, a popular measurement for the research quality of academic researchers. Although the h-index integrates the number of publications and the academic impact of each publication to evaluate the productivity of a researcher, it assumes that all papers that cite an academic article contribute equally to the academic impact of this article. This assumption, of course, could not be true in most times. The citation from a well-cited paper certainly brings more attention to the article than the citation from a paper that people do not pay attention to. It therefore becomes important to integrate the impact of papers that cite a researcher’s work into the evaluation of the productivity of the researcher. Constructing a citation network among academic papers, this paper therefore proposes h _l -index that integrating the h-index with the concept of lobby index, a measures that has been used to evaluate the impact of a node in a complex network based on the impact of other nodes that the focal node has direct link with. This paper also explores the characteristics of the proposed h _l -index by comparing it with citations, h-index and its variant g-index.     

Detecting <Emphasis Type="Italic">h</Emphasis>-index manipulation through self-citation analysis

The h-index has received an enormous attention for being an indicator that measures the quality of researchers and organizations. We investigate to what degree authors can inflate their h-index through strategic self-citations with the help of a simulation. We extended Burrell’s publication model with a procedure for placing self-citations, following three different strategies: random self-citation, recent self-citations and h-manipulating self-citations. The results show that authors can considerably inflate their h-index through self-citations. We propose the q-index as an indicator for how strategically an author has placed self-citations, and which serves as a tool to detect possible manipulation of the h-index. The results also show that the best strategy for an high h-index is publishing papers that are highly cited by others. The productivity has also a positive effect on the h-index.     

The iCE approach for journal evaluation

Recent research has shown that simple graphical representations of research performance can be obtained using two-dimensional maps based on impact (i) and citations (C). The product of impact and citations leads to an energy term (E). Indeed, using E as the third coordinate, three-dimensional landscape maps can be prepared. In this paper, instead of using the traditional impact factor and total citations received for journal evaluation, Article Influence^TM and Eigenfactor^TM are used as substitutes. Article Influence becomes a measure of quality (i.e. a proxy for impact factor) and Eigenfactor is a proxy for size/quantity (like citations) and taken together, the product is an energy-like term. This can be used to measure the influence/prestige of a journal. It is also possible to propose a p-factor (where p = E ^1/3) as an alternative measure of the prestige or prominence of a journal which plays the equivalent role of the h-index.     

The stability of the <Emphasis Type="Italic">h</Emphasis>-index

Over the last years the h-index has gained popularity as a measure for comparing the impact of scientists. We investigate if ranking according to the h-index is stable with respect to (i) different choices of citation databases, (ii) normalizing citation counts by the number of authors or by removing self-citations, (iii) small amounts of noise created by randomly removing citations or publications and (iv) small changes in the definition of the index. In experiments for 5,283 computer scientists and 1,354 physicists we show that although the ranking of the h-index is stable under most of these changes, it is unstable when different databases are used. Therefore, comparisons based on the h-index should only be trusted when the rankings of multiple citation databases agree.     

Comparison of Brazilian researchers in clinical medicine: are criteria for ranking well-adjusted?

Quantifying the relative performance of individual scholars has become an integral part of decision-making in research policy. The objective of the present study was to evaluate if the scholarship rank of Brazilian Council for Scientific and Technological Development (CNPq) researchers in Medicine is consistent with their scientific productivity. The Lattes curricula of 411 researchers (2006–2008) were included in the study. Scholarship category was the variable of interest. Other variables analyzed were: time since receiving the doctorate, teaching activity (undergraduate, master’s and doctoral students), number of articles published, and number of papers indexed by the Institute for Scientific Information (ISI) and Scopus databases. Additional performance indicators included were: citations, h-index, and m-index. There was a significant difference among scholarship categories regarding number of papers per year, considering the entire scientific career (P < 0.001) or the last 5 years (P < 0.001). There was no significant difference among scholarship categories regarding the number of citations per article in the ISI (Thomson Reuters) database (P = 0.23). There was a significant difference in h-index among scholarship categories in both databases, i.e. (P < 0.001) and Scopus (P < 0.001). Regarding the m-index, there was a significant difference among categories only in the ISI database (P = 0.012). According to our findings, a better instrument for qualitative and quantitative indicators is needed to identify researchers with outstanding scientific output.     

Journal Impact Factors for evaluating scientific performance: use of <Emphasis Type="Italic">h</Emphasis>-<Emphasis Type="Italic">like</Emphasis> indicators

This article introduces the Impact Factor squared or IF²-index, an h-like indicator of research performance. This indicator reflects the degree to which large entities such as countries and/or their states participate in top-level research in a field or subfield. The IF²-index uses the Journal Impact Factor (JIF) of research publications instead of the number of citations. This concept is applied to other h-type indexes and their results compared to the IF²-index. These JIF-based indexes are then used to assess the overall performance of cancer research in Australia and its states over 8 years from 1999 to 2006. The IF²-index has three advantages when evaluating larger research units: firstly, it provides a stable value that does not change over time, reflecting the degree to which a research unit participated in top-level research in a given year; secondly, it can be calculated closely approximating the publication date of yearly datasets; and finally, it provides an additional dimension when a full article-based citation analysis is not feasible. As the index reflects the degree of participation in top-level research it may favor larger units when units of different sizes are compared.     

On the relationship between citations of publication output and Hirsch index h of authors: conceptualization of tapered Hirsch index h T, circular citation area radius R and citation acceleration a

The nature of the empirical proportionality constant A in the relation L = Ah ² between total number of citations L of the publication output of an author and his/her Hirsch index h is analyzed using data of the publication output and citations for six scientists elected to the membership of the Royal Society in 2006 and 199 professors working in different institutions in Poland. The main problem with the h index of different authors calculated by using the above relation is that it underestimates the ranking of scientists publishing papers receiving very high citations and results in high values of A. It was found that the value of the Hirsch constant A for different scientists is associated with the discreteness of h and is related to the tapered Hirsch index h _T by A ^1/2 ≈ 1.21h _T. To overcome the drawback of a wide range of A associated with the discreteness of h for different authors, a simple index, the radius R of circular citation area, defined as R = (L/π)^1/2 ≈ h, is suggested. This circular citation area radius R is easy to calculate and improves the ranking of scientists publishing high-impact papers. Finally, after introducing the concept of citation acceleration a = L/t ² = π(R/t)² (t is publication duration of a scientist), some general features of citations of publication output of Polish professors are described in terms of their citability. Analysis of the data of Polish professors in terms of citation acceleration a shows that: (1) the citability of the papers of a majority of physics and chemistry professors is much higher than that of technical sciences professors, and (2) increasing fraction of conference papers as well as non-English papers and engagement in administrative functions of professors result in decreasing citability of their overall publication output.