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 compared. These findings provide a strong validation of $c_f$ as an unbiased indicator for citation performance across disciplines and years. Based on this indicator, we introduce a generalization of the h-index suitable for comparing scientists working in different fields.
Radicchi, Fortunato, and Castellano [arXiv:0806.0974, PNAS 105(45), 17268] claim that, apart from a scaling factor, all fields of science are characterized by the same citation distribution. We present a large-scale validation study of this universality-of-citation-distributions claim. Our analysis shows that claiming citation distributions to be universal for all fields of science is not warranted. Although many fields indeed seem to have fairly similar citation distributions, there are quite some exceptions as well. We also briefly discuss the consequences of our findings for the measurement…
Universality or near-universality of citation distributions was found empirically a decade ago but its theoretical justification has been lacking so far. Here, we systematically study citation distributions for different disciplines in order to characterize this putative universality and to understand it theoretically. Using our calibrated model of citation dynamics, we find microscopic explanation of the universality of citation distributions and explain deviations therefrom. We demonstrate that citation count of the paper is determined, on the one hand, by its fitness -- the attribute which,…
We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations ('classics') are cited mainly by the indirect mechanism. The indirect mechanism gives a po…
To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on copying/redirection/triadic closure mechanism. In a complementary and coherent way, the model accounts both for statistics of references of scientific papers and for their citation dynamics. Originating in empirical measurements, the model is cast in such a way that it can be verified quantitatively …
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 $K$-index has several advantages over Hirsh's $h$-index and, in previous studies, has shown better correlation with Nobel prizes than any other index given by the {\em Web of Science}, including the $h$-index. It is plausible that researchers who are the most connected to other scientifically well-connected researchers are the most likely to be doing important wor…
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 o…
We demonstrate a comprehensive framework that accounts for citation dynamics of scientific papers and for the age distribution of references. We show that citation dynamics of scientific papers is nonlinear and this nonlinearity has far-reaching consequences, such as diverging citation distributions and runaway papers. We propose a nonlinear stochastic dynamic model of citation dynamics based on link copying/redirection mechanism. The model is fully calibrated by empirical data and does not contain free parameters. This model can be a basis for quantitative probabilistic prediction of citation…
Citations measure the importance of a publication, and may serve as a proxy for its popularity and quality of its contents. Here we study the distributions of citations to publications from individual academic institutions for a single year. The average number of citations have large variations between different institutions across the world, but the probability distributions of citations for individual institutions can be rescaled to a common form by scaling the citations by the average number of citations for that institution. We find this feature seem to be universal for a broad selection o…
The journal structure in the China Scientific and Technical Papers and Citations Database (CSTPCD) is analysed from three perspectives: the database level, the specialty level and the institutional level (i.e., university journals versus journals issued by the Chinese Academy of Sciences). The results are compared with those for (Chinese) journals included in the Science Citation Index. The frequency of journal-journal citation relations in the CSTPCD is an order of magnitude lower than in the SCI. Chinese journals, especially high-quality journals, prefer to cite international journals rather…
The large amount of information contained in bibliographic databases has recently boosted the use of citations, and other indicators based on citation numbers, as tools for the quantitative assessment of scientific research. Citations counts are often interpreted as proxies for the scientific influence of papers, journals, scholars, and institutions. However, a rigorous and scientifically grounded methodology for a correct use of citation counts is still missing. In particular, cross-disciplinary comparisons in terms of raw citation counts systematically favors scientific disciplines with high…
We find evidence for the universality of two relative bibliometric indicators of the quality of individual scientific publications taken from different data sets. One of these is a new index that considers both citation and reference counts. We demonstrate this universality for relatively well cited publications from a single institute, grouped by year of publication and by faculty or by department. We show similar behaviour in publications submitted to the arXiv e-print archive, grouped by year of submission and by sub-archive. We also find that for reasonably well cited papers this distribut…
Citation numbers are extensively used for assessing the quality of scientific research. The use of raw citation counts is generally misleading, especially when applied to cross-disciplinary comparisons, since the average number of citations received is strongly dependent on the scientific discipline of reference of the paper. Measuring and eliminating biases in citation patterns is crucial for a fair use of citation numbers. Several numerical indicators have been introduced with this aim, but so far a specific statistical test for estimating the fairness of these numerical indicators has not b…
In this paper we present a phenomenological approach to describe a complex system: scientific research impact through Citation Mining. The novel concept of Citation Mining, a combination of citation bibliometrics and text mining, is used for the phenomenological description. Citation Mining starts with a group of core papers whose impact is to be examined, retrieves the papers that cite these core papers, and then analyzes the technical infrastructure (authors, jorunals, institutions) of the citing papers as well as their thematic characteristics.
The study of the citation histories and ageing of documents are topics that have been addressed from several perspectives, especially in the analysis of documents with delayed recognition or sleeping beauties. However, there is no general methodology that can be extensively applied for different time periods and/or research fields. In this paper a new methodology for the general analysis of the ageing and durability of scientific papers is presented. This methodology classifies documents into three general types: Delayed documents, which receive the main part of their citations later than norm…
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…
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…
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…
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…
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 …
Collaborations and citations within scientific research grow simultaneously and interact dynamically. Modelling the coevolution between them helps to study many phenomena that can be approached only through combining citation and coauthorship data. A geometric graph for the coevolution is proposed, the mechanism of which synthetically expresses the interactive impacts of authors and papers in a geometrical way. The model is validated against a data set of papers published on PNAS during 2007-2015. The validation shows the ability to reproduce a range of features observed with citation and coau…
We analyze the citation time-series of manuscripts in three different fields of science; physics, social science and technology. The evolution of the time-series of the yearly number of citations, namely the citation trajectories, diffuse anomalously, their variance scales with time $\propto t^{2H}$, where $H\neq 1/2$. We provide detailed analysis of the various factors that lead to the anomalous behavior: non-stationarity, long-ranged correlations and a fat-tailed increment distribution. The papers exhibit high degree of heterogeneity, across the various fields, as the statistics of the highe…
Aggregated journal-journal citation networks based on the Journal Citation Reports 2004 of the Science Citation Index (5968 journals) and the Social Science Citation Index (1712 journals) are made accessible from the perspective of any of these journals. The user is thus able to analyze the citation environment in terms of links and graphs. Furthermore, the local impact of a journal is defined as its share of the total citations in the specific journal's citation environments; the vertical size of the nodes is varied proportionally to this citation impact. The horizontal size of each node can …
The relationship of scientific knowledge development to technological development is widely recognized as one of the most important and complex aspects of technological evolution. This paper adds to our understanding of the relationship through use of a more rigorous structure for differentiating among technologies based upon technological domains (defined as consisting of the artifacts over time that fulfill a specific generic function using a specific body of technical knowledge).
This paper analyzes the effect of interdisciplinarity on the scientific impact of individual papers. Using all the papers published in Web of Science in 2000, we define the degree of interdisciplinarity of a given paper as the percentage of its cited references made to journals of other disciplines. We show that, although for all disciplines combined there is no clear correlation between the level of interdisciplinarity of papers and their citation rates, there are nonetheless some disciplines in which a higher level of interdisciplinarity is related to a higher citation rates. For other disci…
Traditionally, the number of citations that a scholarly paper receives from other papers is used as the proxy of its scientific impact. Yet citations can come from domains outside the scientific community, and one such example is through patented technologies---paper can be cited by patents, achieving technological impact. While the scientific impact of papers has been extensively studied, the technological aspect remains less known in the literature. Here we aim to fill this gap by presenting a comparative study on how 919 thousand biomedical papers are cited by U.S. patents and by other pape…
The lack of predictability of citation-based measures frequently used to gauge impact, from impact factors to short-term citations, raises a fundamental question: Is there long-term predictability in citation patterns? Here, we derive a mechanistic model for the citation dynamics of individual papers, allowing us to collapse the citation histories of papers from different journals and disciplines into a single curve, indicating that all papers tend to follow the same universal temporal pattern. The observed patterns not only help us uncover basic mechanisms that govern scientific impact but al…
This paper analyses the influence of geographic distance on knowledge flows, measured through citations to scientific publications. Previous works using the same approach are limited to single disciplines. In this study, we analyse the Italian scientific production in all disciplines matured in the period 2010-2012. To calculate the geographic distances between citing and cited publications, each one is associated with a "prevalent" territory on the basis of the authors' affiliations. The results of the application of a gravity model, estimated using ordinary least squares regression, show tha…
For several decades, a leading paradigm of how to quantitatively assess scientific research has been the analysis of the aggregated citation information in a set of scientific publications. Although the representation of this information as a citation network has already been coined in the 1960s, it needed the systematic indexing of scientific literature to allow for impact metrics that actually made use of this network as a whole improving on the then prevailing metrics that were almost exclusively based on the number of direct citations. However, besides focusing on the assignment of credit,…
The aggregated citation relations among journals included in the Science Citation Index provide us with a huge matrix which can be analyzed in various ways. Using principal component analysis or factor analysis, the factor scores can be used as indicators of the position of the cited journals in the citing dimensions of the database. Unrotated factor scores are exact, and the extraction of principal components can be made stepwise since the principal components are independent. Rotation may be needed for the designation, but in the rotated solution a model is assumed. This assumption can be le…
Citation distributions for 1992, 1994, 1996, 1997, 1999, and 2001, which were published in the 2004 report of the National Science Foundation, USA, are analyzed. It is shown that the ratio of the total number of citations of any two broad fields of science remains close to constant over the analyzed years. Based on this observation, normalization of total numbers of citations with respect to the number of citations in mathematics is suggested as a tool for comparing scientific impact expressed by the number of citations in different fields of science.
Problems for evaluation and impact of published scientific works and their authors are discussed. The role of citations in this process is pointed out. Different bibliometric indicators are reviewed in this connection and ways for generation of new bibliometric indices are given. The influence of different circumstances, like self-citations, number of authors, time dependence and publication types, on the evaluation and impact of scientific papers are considered. The repercussion of works citations and their content is investigated in this respect. Attention is paid also on implicit citations …
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…
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…
Citation based measures are widely used as quantitative proxies for subjective factors such as the importance of a paper or even the worth of individual researchers. Here we analyze the citation histories of $4669$ papers published in journals of the American Physical Society between $1960$ and $1968$ and argue that state-of-the-art models of citation dynamics and algorithms for forecasting nonstationary time series are very likely to fail to predict the long-term ($50$ years after publication) citation counts of highly-cited papers using citation data collected in a short period (say, $10$ ye…
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…
Memes are the cultural equivalent of genes that spread across human culture by means of imitation. What makes a meme and what distinguishes it from other forms of information, however, is still poorly understood. Our analysis of memes in the scientific literature reveals that they are governed by a surprisingly simple relationship between frequency of occurrence and the degree to which they propagate along the citation graph. We propose a simple formalization of this pattern and we validate it with data from close to 50 million publication records from the Web of Science, PubMed Central, and t…
The goal of our research is to understand how ideas propagate, combine and are created in large social networks. In this work, we look at a sample of relevant scientific publications in the area of high-frequency analog circuit design and their citation distribution. A novel aspect of our work is the way in which we categorize citations based on the reason and place of it in a publication. We created seven citation categories from general domain references, references to specific methods used in the same domain problem, references to an analysis method, references for experimental comparison a…
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…
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…
Several network growth models have been proposed in the literature that attempt to incorporate properties of citation networks. Generally, these models aim at retaining the degree distribution observed in real-world networks. In this work, we explore whether existing network growth models can realize the diversity in citation growth exhibited by individual papers - a new node-centric property observed recently in citation networks across multiple domains of research. We theoretically and empirically show that the network growth models which are solely based on degree and/or intrinsic fitness c…
We analyze the online response to the preprint publication of a cohort of 4,606 scientific articles submitted to the preprint database arXiv.org between October 2010 and May 2011. We study three forms of responses to these preprints: downloads on the arXiv.org site, mentions on the social media site Twitter, and early citations in the scholarly record. We perform two analyses. First, we analyze the delay and time span of article downloads and Twitter mentions following submission, to understand the temporal configuration of these reactions and whether one precedes or follows the other. Second,…
Citation count is a popular index for assessing scientific papers. However, it depends on not only the quality of a paper but also various factors, such as conventionality, team size, and gender. Here, we examine the extent to which the conventionality of a paper is related to its citation percentile in a discipline by using our measure, topic disparity. The topic disparity is the cosine distance between a paper and its discipline on a neural embedding space. Using this measure, we show that the topic disparity is negatively associated with the citation percentile in many disciplines, even aft…
The aggregated journal-journal citation matrix -based on the Journal Citation Reports (JCR) of the Science Citation Index- can be decomposed by indexers and/or algorithmically. In this study, we test the results of two recently available algorithms for the decomposition of large matrices against two content-based classifications of journals: the ISI Subject Categories and the field/subfield classification of Glaenzel & Schubert (2003). The content-based schemes allow for the attribution of more than a single category to a journal, whereas the algorithms maximize the ratio of within-category ci…
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 …
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…
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 …
In addition to science citation indicators of journals like impact and immediacy, social network analysis provides a set of centrality measures like degree, betweenness, and closeness centrality. These measures are first analyzed for the entire set of 7,379 journals included in the Journal Citation Reports of the Science Citation Index and the Social Sciences Citation Index 2004, and then also in relation to local citation environments which can be considered as proxies of specialties and disciplines. Betweenness centrality is shown to be an indicator of the interdisciplinarity of journals, bu…
In a range of citation networks, the in-degree distributions boast time-periodicity---the distributions of citations per article published each year present similar scale-free tails. This phenomenon can be regarded as a consequence of the emergence of hot topics and the existence of the "burst" phenomenon. With this inference considered, a geometric model based on our previous study is established, in which the sizes of the influence zones of nodes follow the same power-law distribution and decrease with their ages. The model successfully reproduces the time-periodicity of the in-degree distri…
Structural inequalities persist in society, conferring systematic advantages to some people at the expense of others, for example, by giving them substantially more influence and opportunities. Using bibliometric data about authors of scientific publications, we identify two types of structural inequalities in scientific citations. First, female authors, who represent a minority of researchers, receive less recognition for their work (through citations) relative to male authors; second, authors affiliated with top-ranked institutions, who are also a minority, receive substantially more recogni…
Academic papers have been the protagonists in disseminating expertise. Naturally, paper citation pattern analysis is an efficient and essential way of investigating the knowledge structure of science and technology. For decades, it has been observed that citation of scientific literature follows a heterogeneous and heavy-tailed distribution, and many of them suggest a power-law distribution, log-normal distribution, and related distributions. However, many studies are limited to small-scale approaches; therefore, it is hard to generalize. To overcome this problem, we investigate 21 years of ci…
Many innovations are inspired by past ideas in a non-trivial way. Tracing these origins and identifying scientific branches is crucial for research inspirations. In this paper, we use citation relations to identify the descendant chart, i.e. the family tree of research papers. Unlike other spanning trees which focus on cost or distance minimization, we make use of the nature of citations and identify the most important parent for each publication, leading to a tree-like backbone of the citation network. Measures are introduced to validate the backbone as the descendant chart. We show that cita…
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,…
We review our recent work on applying the Google PageRank algorithm to find scientific "gems" among all Physical Review publications, and its extension to CiteRank, to find currently popular research directions. These metrics provide a meaningful extension to traditionally-used importance measures, such as the number of citations and journal impact factor. We also point out some pitfalls of over-relying on quantitative metrics to evaluate scientific quality.
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…
We investigate how textual properties of scientific papers relate to the number of citations they receive. Our main finding is that correlations are non-linear and affect differently most-cited and typical papers. For instance, we find that in most journals short titles correlate positively with citations only for the most cited papers, for typical papers the correlation is in most cases negative. Our analysis of 6 different factors, calculated both at the title and abstract level of 4.3 million papers in over 1500 journals, reveals the number of authors, and the length and complexity of the a…
For decades the number of scientific publications has been rapidly increasing, effectively out-dating knowledge at a tremendous rate. Only few scientific milestones remain relevant and continuously attract citations. Here we quantify how long scientific work remains being utilized, how long it takes before today's work is forgotten, and how milestone papers differ from those forgotten. To answer these questions, we study the complete temporal citation network of all American Physical Society journals. We quantify the probability of attracting citations for individual publications based on age …
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 social recognition. Indeed, the $K$-index measures the number of hubs, defined in a self-consistent way in the bipartite network, that cites a given author. We show that the $K$-index can be computed by simple inspection of the Web of Science platform and presents several advantages over other centrality indexes, in particular Hirsch $h$-index. The $K$-index is…
Is more always better? We address this question in the context of bibliometric indices that aim to assess the scientific impact of individual researchers by counting their number of highly cited publications. We propose a simple model in which the number of citations of a publication depends not only on the scientific impact of the publication but also on other 'random' factors. Our model indicates that more need not always be better. It turns out that the most influential researchers may have a systematically lower performance, in terms of highly cited publications, than some of their less in…
