The average age at which U.S. researchers get their first grant from NIH has increased from 34.3 in 1970, to 41.7 in 2004. These data raise the crucial question of the effects of aging on the scientific creativity and productivity of researchers. Those who worry about the aging of scientists usually believe that the younger they are the more creative and productive they will be. Using a large population of 13,680 university professors in Quebec, we show that, while scientific productivity rises sharply between 28 and 40, it increases at a slower pace between 41 and 50 and stabilizes afterward until retirement for the most active researchers. The average scientific impact per paper decreases linearly until 50-55 years old, but the average number of papers in highly cited journals and among highly cited papers rises continuously until retirement. Our results clearly show for the first time the natural history of the scientific productivity of scientists over their entire career and bring to light the fact that researchers over 55 still contribute significantly to the scientific community by producing high impact papers.
Growing network models with preferential attachment dependent on both age and degree are proposed to simulate certain features of citation network noted in \cite{red2}. In this directed network, a new node gets attached to an older node with the probability $\sim K(k)f(t)$ where the degree and age of the older node are $k$ and $t$ respectively. Several functional forms of $K(k)$ and $f(t)$ have been considered. The desirable features of the citation network can be reproduced with $K(k) \sim k^{-β}$ and $f(t) \sim \exp(αt)$ with $β=2.0$ and $α= -0.2$ and with simple modifications in the growth …
As a simple means for comparing and - if possible - predicting scientific impacts of different researchers working in the same field, we suggest comparing their "sales curves". A sales curve is the number of citations of the researcher's papers per year, the citation rate, considered as a function of time. As examples, we present the citation histories of 10 older well-cited scientists working in the same field. The sales curve is found to be highly individual, that is, there is a large variation between different scientists' sales curves. For each well-cited scientist, however, the sales curv…
The study of citation networks is of interest to the scientific community. However, the underlying mechanism driving individual citation behavior remains imperfectly understood, despite the recent proliferation of quantitative research methods. Traditional network models normally use graph theory to consider articles as nodes and citations as pairwise relationships between them. In this paper, we propose an alternative evolutionary model based on hypergraph theory in which one hyperedge can have an arbitrary number of nodes, combined with an aging effect to reflect the temporal dynamics of sci…
A scheme of evaluating an impact of a given scientific paper based on importance of papers quoting it is investigated. Introducing a weight of a given citation, dependent on the previous scientific achievements of the author of the citing paper, we define the weighting factor of a given scientist. Technically the weighting factors are defined by the components of the normalized leading eigenvector of the matrix describing the citation graph. The weighting factor of a given scientist, reflecting the scientific output of other researchers quoting his work, allows us to define weighted number of …
A multi-parametric family of stretch exponential distributions with various power law tails is introduced and is shown to describe adequately the empirical distributions of scientific citation of individual authors. The four-parametric families are characterized by a normalization coefficient in the exponential part, the power exponent in the power-law asymptotic part, and the coefficient for the transition between the above two parts. The distribution of papers of individual scientist over citations of these papers is studied. Scientists are selected via total number of citations in three ran…
We analyze the time evolution of citations acquired by articles from journals of the American Physical Society (PRA, PRB, PRC, PRD, PRE and PRL). The observed change over time in the number of papers published in each journal is considered an exogenously caused variation in citability that is accounted for by a normalization. The appropriately inflation-adjusted citation rates are found to be separable into a preferential-attachment-type growth kernel and a purely obsolescence-related (i.e., monotonously decreasing as a function of time since publication) aging function. Variations in the empi…
In recent years, the relationship of collaboration among scientists and the citation impact of papers have been frequently investigated. Most of the studies show that the two variables are closely related: an increasing collaboration activity (measured in terms of number of authors, number of affiliations, and number of countries) is associated with an increased citation impact. However, it is not clear whether the increased citation impact is based on the higher quality of papers which profit from more than one scientist giving expert input or other (citation-specific) factors. Thus, the curr…
h-index has become the most popular indicator for quantifying a scientist's scientific impact in various scientific fields. h-index is defined as the largest number of papers with citation number larger than or equal to h and it treats each citation equally. However, different citations usually come from different papers with different influence and quality, and a citation from a highly influential paper is a greater recognition of the target paper than a citation from an ordinary paper. Based on this assumption, we proposed a new indicator named x-index to quantify a scientist's scientific im…
The number of citations is a widely used metric to evaluate the scientific credit of papers, scientists and journals. However, it does happen that a paper with fewer citations from prestigious scientists is of higher influence than papers with more citations. In this paper, we argue that from whom the paper is being cited is of higher significance than merely the number of received citations. Accordingly, we propose an interactive model on author-paper bipartite networks as well as an iterative algorithm to get better rankings for scientists and their publications. The main advantage of this m…
Appraisal of the scientific impact of researchers, teams and institutions with productivity and citation metrics has major repercussions. Funding and promotion of individuals and survival of teams and institutions depend on publications and citations. In this competitive environment, the number of authors per paper is increasing and apparently some co-authors don't satisfy authorship criteria. Listing of individual contributions is still sporadic and also open to manipulation. Metrics are needed to measure the networking intensity for a single scientist or group of scientists accounting for pa…
Recent "science of science" research shows that scientific impact measures for journals and individual articles have quantifiable regularities across both time and discipline. However, little is known about the scientific impact distribution at the scale of an individual scientist. We analyze the aggregate scientific production and impact of individual careers using the rank-citation profile c_{i}(r) of 200 distinguished professors and 100 assistant professors. For the entire range of paper rank r, we fit each c_{i}(r) to a common distribution function that is parameterized by two scaling expo…
h-index retrieved by citation indexes (Scopus, Google scholar, and Web of Science) is used to measure the scientific performance and the research impact studies based on the number of publications and citations of a scientist. It also is easily available and may be used for performance measures of scientists, and for recruitment decisions. The aim of this study is to investigate the difference between the outputs and results from these three citation databases namely Scopus, Google Scholar, and Web of Science based upon the h-index of a group of highly cited researchers (Nobel Prize winner sci…
Academic success is distributed unequally; a few top scientists receive the bulk of attention, citations, and resources. However, do these ``superstars" foster leadership in scientific innovation? We introduce three information-theoretic measures that quantify novelty, innovation, and impact from scholarly citation networks, and compare the scholarly output of scientists who are either not connected or strongly connected to superstar scientists. We find that while connected scientists do indeed publish more, garner more citations, and produce more diverse content, this comes at a cost of lower…
This Brief Communication discusses the benefits of citation analysis in research evaluation based on Galton's "Wisdom of Crowds" (1907). Citations are based on the assessment of many which is why they can be ascribed a certain amount of accuracy. However, we show that citations are incomplete assessments and that one cannot assume that a high number of citations correlate with a high level of usefulness. Only when one knows that a rarely cited paper has been widely read is it possible to say (strictly speaking) that it was obviously of little use for further research. Using a comparison with '…
Publication statistics are ubiquitous in the ratings of scientific achievement, with citation counts and paper tallies factoring into an individual's consideration for postdoctoral positions, junior faculty, tenure, and even visa status for international scientists. Citation statistics are designed to quantify individual career achievement, both at the level of a single publication, and over an individual's entire career. While some academic careers are defined by a few significant papers (possibly out of many), other academic careers are defined by the cumulative contribution made by the auth…
We have developed a method to obtain robust quantitative bibliometric indicators for several thousand scientists. This allows us to study the dependence of bibliometric indicators (such as number of publications, number of citations, Hirsch index...) on the age, position, etc. of CNRS scientists. Our data suggests that the normalized h index (h divided by the career length) is not constant for scientists with the same productivity but differents ages. We also compare the predictions of several bibliometric indicators on the promotions of about 600 CNRS researchers. Contrary to previous publica…
A large number of published studies have examined the properties of either networks of citation among scientific papers or networks of coauthorship among scientists. Here, using an extensive data set covering more than a century of physics papers published in the Physical Review, we study a hybrid coauthorship/citation network that combines the two, which we analyze to gain insight into the correlations and interactions between authorship and citation. Among other things, we investigate the extent to which individuals tend to cite themselves or their collaborators more than others, the extent …
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, because for the majority of scientists analyzed, we find the excess citation fraction (C-h^{2})/C to be distributed closely around the value 0.75, meaning that 75 percent of the author's impact is neglected. Additionally, Z is less sensitive to local changes in a scientist's citation profile, namely perturbations which increase h while only marginally affecting C.…
Computing such correlation coefficient would be straightforward had we had available the rankings given by the prize committee to all scientists in the pool. In reality we only have citation rankings for all scientists. This means, however, that we have the ordinal rankings of the prize winners with regard to citation metrics. I use maximum likelihood method to infer the most probable correlation coefficient to produce the observed pattern of ordinal ranks of the prize winners. I get the correlation coefficients of 0.47 and 0.59 between the composite citation indicator and getting Abel Prize a…
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 o…
Scientists are embedded in social and information networks that influence and are influenced by the quality of their scientific work, its impact, and the recognition they receive. Here we quantify the systematic relationship between a scientist's position in the network of scientific collaborations and the citations they receive. As expected, we find that authors closer to others in this network are, on average, more highly cited than those further away from others. We construct a novel indicator, the s-index, that explicitly captures performance linked to network position along two compliment…
Despite the huge amount of literature on h-index, few papers have been devoted to the statistical analysis of h-index when a probabilistic distribution is assumed for citation counts. The present contribution relies on showing the available inferential techniques, by providing the details for proper point and set estimation of the theoretical h-index. Moreover, some issues on simultaneous inference - aimed to produce suitable scholar comparisons - are carried out. Finally, the analysis of the citation dataset for the Nobel Laureates (in the last five years) and for the Fields medallists (from …
The concept of h-index has been proposed to easily assess a researcher's performance with a single number. However, by using only this number, we lose significant information about the distribution of citations per article in an author's publication list. In this article, we study an author's citation curve and we define two new areas related to this curve. We call these "penalty areas", since the greater they are, the more an author's performance is penalized. We exploit these areas to establish new indices, namely PI and XPI, aiming at categorizing researchers in two distinct categories: "in…
We propose a model of the evolution of the networks of scientific citations. The model takes an out-degree distribution (distribution of number of citations) and two parameters as input. The parameters capture the two main ingredients of the model, the aging of the relevance of papers and the formation of triangles when new papers cite old. We compare our model with three network structural quantities of an empirical citation network. We find that an unique point in parameter space optimizing the match between the real and model data for all quantities. The optimal parameter values suggest tha…
It has recently been claimed by Baccini and coauthors that due to ANVUR's bibliometric evaluations of individuals, departments, and universities, in Italy there has been a surge in self-citations in the last ten years, thus increasing the "inwardness" of Italian research more than has happened abroad. We have studied the database of Ioannidis et al. published on 12 August 2019 of the one hundred thousand most "highly cited" scientists, including about two thousand Italians, and we found that the problem of self-citations in relation to this scientific elite is not significant in Italy, while p…
Quantitative bibliometric indicators are widely used to evaluate the performance of scientists. However, traditional indicators do not much rely on the analysis of the processes intended to measure and the practical goals of the measurement. In this study, I propose a simple framework to measure and predict an individual researcher's scientific performance that takes into account the main regularities of publication and citation processes and the requirements of practical tasks. Statistical properties of the new indicator - a scientist's personal impact rate - are illustrated by its applicatio…
Recent research has found that select scientists have a disproportional share of highly cited papers. Researchers reasoned that this could not have happened if success in science was random and introduced a hidden parameter Q, or talent, to explain this finding. So, the talented high-Q scientists have many high impact papers. Here I show that an upgrade of an old random citation copying model could also explain this finding. In the new model the probability of citation copying is not the same for all papers but is proportional to the logarithm of the total number of citations to all papers of …
Reputation is an important social construct in science, which enables informed quality assessments of both publications and careers of scientists in the absence of complete systemic information. However, the relation between reputation and career growth of an individual remains poorly understood, despite recent proliferation of quantitative research evaluation methods. Here we develop an original framework for measuring how a publication's citation rate $Δc$ depends on the reputation of its central author $i$, in addition to its net citation count $c$. To estimate the strength of the reputatio…
Analysis of citation records of 52 active and productive condensed matter physicists shows that the ratio of h-index to the mean age of h most highly cited publications is a reliable quantity that allows meaningful comparison of scientists of different age.
Recently, the abundance of digital data enabled the implementation of graph based ranking algorithms that provide system level analysis for ranking publications and authors. Here we take advantage of the entire Physical Review publication archive (1893-2006) to construct authors' networks where weighted edges, as measured from opportunely normalized citation counts, define a proxy for the mechanism of scientific credit transfer. On this network we define a ranking method based on a diffusion algorithm that mimics the spreading of scientific credits on the network. We compare the results obtain…
Studies of bibliographic data suggest a strong correlation between the growth of citation networks and their corresponding co-authorship networks. We explore the interdependence between evolving citation and co-authorship networks focused on the publications, by Indian authors, in American Physical Society journals between 1970 and 2013. We record interactions between each possible pair of authors in two ways: first, by tracing the change in citations they exchanged and, second, by tracing the shortest path between authors in the co-authorship network. We create these data for every year of th…
We analyze the publication records of individual scientists, aiming to quantify the topic switching dynamics of scientists and its influence. For each scientist, the relations among her publications are characterized via shared references. We find that the co-citing network of the papers of a scientist exhibits a clear community structure where each major community represents a research topic. Our analysis suggests that scientists tend to have a narrow distribution of the number of topics. However, researchers nowadays switch more frequently between topics than those in the early days. We also…
The rapid evolution of scientific research has been creating a huge volume of publications every year. Among the many quantification measures of scientific impact, citation count stands out for its frequent use in the research community. Although peer review process is the mainly reliable way of predicting a paper's future impact, the ability to foresee lasting impact on the basis of citation records is increasingly important in the scientific impact analysis in the era of big data. This paper focuses on the long-term citation count prediction for individual publications, which has become an e…
During the last decade, we have witnessed a sustained growth of South Korea's research output in terms of the world share of publications in the Science Citation Index database. However, Korea's citation performance is not yet as competitive as publication performance. In this study, the authors examine the intellectual structure of Korean S&T field based on social network analysis of journal-journal citation data using the ten Korean SCI journals as seed journals. The results reveal that Korean SCI journals function more like publication places, neither research channels nor information sourc…
Recently we proposed a model in which when a scientist writes a manuscript, he picks up several random papers, cites them and also copies a fraction of their references (cond-mat/0305150). The model was stimulated by our discovery that a majority of scientific citations are copied from the lists of references used in other papers (cond-mat/0212043). It accounted quantitatively for several properties of empirically observed distribution of citations. However, important features, such as power-law distribution of citations to papers published during the same year and the fact that the average ra…
Old and recent theoretical works by Andrzej Pekalski (APE) are recalled as possible sources of interest for describing network formation and clustering in complex (scientific) communities, through self-organisation and percolation processes. Emphasis is placed on APE self-citation network over four decades. The method is that used for detecting scientists field mobility by focusing on author's self-citation, co-authorships and article topics networks as in [1,2]. It is shown that APE's self-citation patterns reveal important information on APE interest for research topics over time as well as …
We study the distributions of citations received by a single publication within several disciplines, spanning broad areas of science. We show that the probability that an article is cited $c$ times has large variations between different disciplines, but all distributions are rescaled on a universal curve when the relative indicator $c_f=c/c_0$ is considered, where $c_0$ is the average number of citations per article for the discipline. In addition we show that the same universal behavior occurs when citation distributions of articles published in the same field, but in different years, are com…
The historical and contemporary under-attribution of women's contributions to scientific scholarship is well-known and well-studied, with effects that are felt today in myriad ways by women scientists. One measure of this under-attribution is the so-called citation gap between men and women: the under-citation of papers authored by women relative to expected rates coupled with a corresponding over-citation of papers authored by men relative to expected rates. We explore the citation gap in contemporary physics, analyzing over one million articles published over the last 25 years in 35 physics …
The basic indicators of a researcher's productivity and impact are still the number of publications and their citation counts. These metrics are clear, straightforward, and easy to obtain. When a ranking of scholars is needed, for instance in grant, award, or promotion procedures, their use is the fastest and cheapest way of prioritizing some scientists over others. However, due to their nature, there is a danger of oversimplifying scientific achievements. Therefore, many other indicators have been proposed including the usage of the PageRank algorithm known for the ranking of webpages and its…
The h-index is a popular bibliometric indicator for assessing individual scientists. We criticize the h-index from a theoretical point of view. We argue that for the purpose of measuring the overall scientific impact of a scientist (or some other unit of analysis) the h-index behaves in a counterintuitive way. In certain cases, the mechanism used by the h-index to aggregate publication and citation statistics into a single number leads to inconsistencies in the way in which scientists are ranked. Our conclusion is that the h-index cannot be considered an appropriate indicator of a scientist's …
Whether a scientific paper is cited is related not only to the influence of its author(s) but also to the journal publishing it. Scientists, either proficient or tender, usually submit their most important work to prestigious journals which receives higher citations than the ordinary. How to model the role of scientific journals in citation dynamics is of great importance. In this paper we address this issue through two folds. One is the intrinsic heterogeneity of a paper determined by the impact factor of the journal publishing it. The other is the mechanism of a paper being cited which depen…
How to quantify the impact of a researcher's or an institution's body of work is a matter of increasing importance to scientists, funding agencies, and hiring committees. The use of bibliometric indicators, such as the h-index or the Journal Impact Factor, have become widespread despite their known limitations. We argue that most existing bibliometric indicators are inconsistent, biased, and, worst of all, susceptible to manipulation. Here, we pursue a principled approach to the development of an indicator to quantify the scientific impact of both individual researchers and research institutio…
Nobel Prizes are commonly seen to be among the most prestigious achievements of our times. Based on mining several million citations, we quantitatively analyze the processes driving paradigm shifts in science. We find that groundbreaking discoveries of Nobel Prize Laureates and other famous scientists are not only acknowledged by many citations of their landmark papers. Surprisingly, they also boost the citation rates of their previous publications. Given that innovations must outcompete the rich-gets-richer effect for scientific citations, it turns out that they can make their way only throug…
Mathematical models of the scientific citation process predict a strong "first-mover" effect under which the first papers in a field will, essentially regardless of content, receive citations at a rate enormously higher than papers published later. Moreover papers are expected to retain this advantage in perpetuity -- they should receive more citations indefinitely, no matter how many other papers are published after them. We test this conjecture against data from a selection of fields and in several cases find a first-mover effect of a magnitude similar to that predicted by the theory. Were w…
Citations are commonly held to represent scientific impact. To date, however, there is no empirical evidence in support of this postulate that is central to research assessment exercises and Science of Science studies. Here, we report on the first empirical verification of the degree to which citation numbers represent scientific impact as it is actually perceived by experts in their respective field. We run a large-scale survey of about 2000 corresponding authors who performed a pairwise impact assessment task across more than 20000 scientific articles. Results of the survey show that citatio…
Evaluating the performance of researchers and measuring the impact of papers written by scientists is the main objective of citation analysis. Various indices and metrics have been proposed for this. In this paper, we propose a new citation index CITEX, which gives normalized scores to authors and papers to determine their rankings. To the best of our knowledge, this is the first citation index which simultaneously assigns scores to both authors and papers. Using these scores, we can get an objective measure of the reputation of an author and the impact of a paper. We model this problem as an …
Understanding the nature and organization of scientific communities is of broad interest. The `Invisible College' is a historical metaphor for one such type of community and the search for such `colleges' can be framed as the detection and analysis of small groups of scientists working on problems of common interests. Case studies have previously been conducted on individual communities with respect to their scientific and social behavior. In this study, we introduce, a new and scalable community finding approach. Supplemented by expert assessment, we use the convergence of two different clust…
A public preprint server such as arXiv allows authors to publish their manuscripts before submitting them to journals for peer review. It offers the chance to establish priority by making the results available upon completion. This article presents the arXiv section Quantitative Biology and investigates the advantages of preprint publications in terms of reception, which can be measured by means of citations. This paper focuses on the publication and citation delay, citation counts and the authors publishing their e-prints on arXiv. Moreover, the paper discusses the benefit for scientists as w…
The $α$ person is the dominant person in a group. We define the $α$-author of a paper as the author of the paper with the highest $h$-index among all the coauthors, and an $α$-paper of a scientist as a paper authored or coauthored by the scientist where he/she is the $α$-author. For most but not all papers in the literature there is only one $α$-author. We define the $h_α$ index of a scientist as the number of papers in the $h$-core of the scientist (i.e. the set of papers that contribute to the $h$-index of the scientist) where this scientist is the $α$-author. We also define the $h'_α$ index…
One of the most interesting scientific challenges nowadays deals with the analysis and the understanding of complex networks' dynamics. A major issue is the definition of new frameworks for the exploration of the dynamics at play in real dynamic networks. Here, we focus on scientific communities by analyzing the "social part" of Science through a descriptive approach that aims at identifying the social determinants (e.g. goals and potential interactions among individuals) behind the emergence and the resilience of scientific communities. We consider that scientific communities are at the same …
A model is proposed for the creation and transmission of scientific knowledge, based on the network of citations among research articles. The model allows to assign to each article a nonnegative value for its creativity, i. e. its creation of new knowledge. If the entire publication network is truncated to the first neighbors of an article (the n references that it makes and the m citations that it receives), its creativity value becomes a simple function of n and m. After splitting the creativity of each article among its authors, the cumulative creativity of an author is then proposed as an …
Progress in science has advanced the development of human society across history, with dramatic revolutions shaped by information theory, genetic cloning, and artificial intelligence, among the many scientific achievements produced in the 20th century. However, the way that science advances itself is much less well-understood. In this work, we study the evolution of scientific development over the past century by presenting an anatomy of 89 million digitalized papers published between 1900 and 2015. We find that science has benefited from the shift from individual work to collaborative effort,…
To account for strong aging characteristics of citation networks, we modify Google's PageRank algorithm by initially distributing random surfers exponentially with age, in favor of more recent publications. The output of this algorithm, which we call CiteRank, is interpreted as approximate traffic to individual publications in a simple model of how researchers find new information. We develop an analytical understanding of traffic flow in terms of an RPA-like model and optimize parameters of our algorithm to achieve the best performance. The results are compared for two rather different citati…
Inspired by the social and economic benefits of diversity, we analyze over 9 million papers and 6 million scientists to study the relationship between research impact and five classes of diversity: ethnicity, discipline, gender, affiliation, and academic age. Using randomized baseline models, we establish the presence of homophily in ethnicity, gender and affiliation. We then study the effect of diversity on scientific impact, as reflected in citations. Remarkably, of the classes considered, ethnic diversity had the strongest correlation with scientific impact. To further isolate the effects o…
