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Universality of citation distributions for academic institutions and journals

Arnab Chatterjee,1, ∗ Asim Ghosh,1, † and Bikas K Chakrabarti1, 2, ‡

1Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 India.2Economic Research Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.

Citations measure the importance of a publication, and may serve as a proxy for its popularity andquality of its contents. Here we study the distributions of citations to publications from individualacademic institutions for a single year. The average number of citations have large variationsbetween different institutions across the world, but the probability distributions of citations forindividual institutions can be rescaled to a common form by scaling the citations by the averagenumber of citations for that institution. We find this feature to be universal for a broad selectionof institutions irrespective of the average number of citations per article. A similar analysis forcitations to publications in a particular journal in a single year reveals that there are at least twodistinct classes of journals across disciplines, depending on the form of the distribution function.We observe that a group of journals with high impact factor and average citations that are distinctfrom the majority of the journals which form a different class.

I. INTRODUCTION

Statistical physics tells us that systems of many interacting dynamical units collectively exhibit, a behavior which isdetermined by only a few basic dynamical features of the individual units and of the embedding dimension, but inde-pendent of all other details. This feature which is specific to critical phenomena, like in continuous phase transitions,is known as universality [1]. There is enough empirical evidence that a number of social phenomena are characterizedby simple emergent behavior out of the interactions of many individuals. In recent years, a growing community ofresearchers have been analyzing large-scale social dynamics to uncover universal patterns and also trying to proposesimple microscopic models to describe them, similar to the minimalistic models used in statistical physics. These stud-ies have revealed interesting patterns and behaviors in social systems, e.g., in elections [2–4], growth in population [5]and economy [6], income and wealth distributions [7], financial markets [8], languages [9], etc. (see Refs. [10, 11] forreviews).Academic publications (papers, books etc.) form an unique social system consisting of individual publications as

entities, containing bibliographic reference to other older publications, and this is commonly termed as citation. Thenumber of citations is a measure of the importance of a publication, and serve as a proxy for the popularity andquality of a publication. There has already been a plethora of empirical studies on citation data [11], specificallyon citation distributions [12–15] of articles, time evolution of probability distribution of citation [16–18], citationsfor individuals [19] and even their dynamics [20], and the modeling efforts on the growth and structure of citationnetworks have produced a huge body literature in network science concerning scale-free networks [21–23].The bibliometric tool of citation analysis is becoming increasingly popular for evaluating the performance of indi-

viduals, research groups, institutions as well as countries, the outcomes of which are becoming important in case ofoffering grants and awards, academic promotions and ranking, as well as jobs in academia, industry and otherwise.Since citations serve as a crucial measure for the importance and impact of a research publication, its precise analysisis extremely important. Annual citations and impact factor of journals are of key interest, primarily from the point ofview of journals themselves, and secondarily from the perspective of authors who publish their papers in them. Widedistributions of both annual citations and impact factors are quite well studied [24–26]. It is quite usual to find thatsome publications do better than others due to the inherent heterogeneity in the quality of their content, the grossattention on the field of research, the relevance to future work and so on. Thus different publications gather citationsin time at different rates and result in a broad distribution of citations. In 1957, Shockley [12] claimed that thescientific publication rate is dictated by a lognormal distribution, while a later evidence based on analysis of recordsfor highly cited physicists claim that the citation distribution of individual authors follow a stretched exponential [13].However, an analysis of data from ISI claims that the tail of the citation distribution of individual publications decaysas a power law with an exponent close to 3 [14], while a rigorous analysis of 110 years of data from Physical Review

∗Email: arnabchat@gmail.com†Email: asim.ghosh@saha.ac.in‡Email: bikask.chakrabarti@saha.ac.in

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concluded that most part of the citation distribution fits remarkably well to a lognormal [27]. The present consensuslies with the fact that while most part of the distribution does fit to a lognormal, the extreme tail fits to a powerlaw [28].It has been shown earlier [29] that the distribution of citations c to papers within a discipline has a broad distribution,

which is universal across broad scientific disciplines, using a relative indicator c/〈c〉, where 〈c〉 is the average citationwithin a discipline. However, it has also been shown later that this universality is not absolutely guaranteed [30].In this article, we focus on citations received by individual (i) academic institutions and (ii) academic journals. While

institutions can vary in their quality of scientific output measurable in terms of total number of publications, totalcitations etc., here we show for the first time that irrespective of the institution’s scientific productivity, ranking andresearch impact, the probability P (c) that the number of citations c received by a publication is a broad distributionwith an universal functional form. In fact, using a relative indicator c/〈c〉, where 〈c〉 is the average number of citationsto articles published by an institution in a certain year, we show that the effective probability distribution functionthat an article has c citations has the same mathematical form. We present strong evidence for the fact that this holdstrue across time for most institutions irrespective of the scientific productivity of the institution considered. When wecarry out a similar analysis on journals, we find that there are, in fact, at least two major categories of distributions.Journals with high impact factor and high average citations have a broad yet strongly monotonic distribution P (c)of citations characterized by 1/c for the lowest values of citations c, form the Elite class, while the majority fall intoa General class, which is again broad but fits nicely to a lognormal distribution for most of its range. We find thatthese features hold true across time and across journals within the same class. The largest citations for academicinstitutions as well as both the classes of journals fit well to a power law.

II. RESULTS

We study the data of number of citations to publications from different years, from ISI Web of Science [31] forseveral (i) academic institutions (research institutes and universities) and (ii) popular journals. It is to be noted thatcitations to individual publications arrive from any publication indexed in ISI Web of Science and does not meanonly internal citations within the journal in which it is published. We analyzed data of science publications from42 academic institutions and 30 popular journals. For institutions, we collected data for publications which have atleast one author who mentions that institution as his/her affiliation. We recorded the data for the number of paperspublished, the total number of citations to each of the publications, for a few years (1980, 1990, 2000, 2010 for mostcases). Since citations grow with time, we have studied publications which are at least 4 years old (from 2010) or more(1980, 1990, 2000) to rule out any role of transients. We also collect data from academic institutions and journalswhich have a comparatively large number of publications, so as to produce good statistics, and minimize the effectsof aberration that can result from fluctuations of the quantities measured from small data sets.

A. Citations for academic institutions

We collected citation data until date for all publications from a particular year (e.g. 1980, 1990, 2000, 2010). Foreach year, the probability distribution P (c) of citations c for an academic institution was observed to be broad. Forinstance, Fig. 1A shows the plot of P (c) vs. c for various institutions for publications from 1990. We rescaled theabsolute value of citation for each year by the average number of citations per publication 〈c〉, and plotted it againstthe adjusted probability 〈c〉P (c) (Fig. 1B) (see similar plots for 1980 and 2000 in Fig. 6 of SI). We remarkably findthat the distributions collapse into an universal curve irrespective of the wide variation in the academic output of thedifferent institutions. The scaling collapse is good for more than 3 decades of data and over 5 orders of magnitude.The average number of papers, total citations and the average number of citations per publication are shown inTable III. The rescaled curves fit well to a lognormal

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FIG. 1: (A) Probability distribution P (c) of citations c to publications from 1990 for several academic institutions. (B) Thesame data rescaled by average number of citations 〈c〉. The data for different institutions seem to follow the same scalingfunction. It fits very well to a lognormal function for most of its range, with µ ≈ −0.73, σ ≈ 1.29. The largest citations do notfollow the lognormal behavior, and seem to follow a power law: c−α, with α = 2.6± 0.4.

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number of citations. Fig. 2 shows the plot for 1990. To check if this also holds for time-aggregated data, we collectedcitations for all papers published during the period 2001-2005 for the same set of institutions, and repeated the aboveanalysis. The universality is even more firmly established (see SI. Fig. 7).

B. Citations for journals

We collected citation data until date for all publications in individual journals for several years (e.g. 1980, 1990,2000, 2010 etc.). For each year, the probability distribution P (c) of citations c was again observed to be broad.We rescaled the absolute value of citation for each year by its average value 〈c〉, and plotted it against the adjustedprobability 〈c〉P (c) (Fig. 3 and Fig. 4). For a particular journal, it is observed that the curves follow the same

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FIG. 3: Probability distribution P (c) of citations c rescaled by average number of citations 〈c〉 to publications from from 4different years (1980, 1990, 2000, 2010) for several academic journals in the General class: For any journal, the data for differentyears seem to follow the same distribution.

distribution over years although the average number of papers, total citations and hence the average number ofcitations vary (See Table IV and Table V in SI for details). Further, we plot the same quantity for a particularyear for different institutions (see Fig. 5 for 1990), and remarkably find that two distinct classes of journals emergeaccording to the shape of the universal distributions to which the curves collapse. The first group is a General class(Fig. 5A), for which most of the distribution fits well to a lognormal function with µ ≈ −0.75 and σ ≈ 1.18, as wasobserved in case of institutions, with 〈c〉P (c) → const. i.e., P (c) ∼ 1/〈c〉 for the lowest values of the abscissa. Theother group, which we call the Elite class (Fig. 5B) is also broadly distributed but has a distinct and faster monotonicdecay compared to the General class, where 〈c〉P (c) ∼ (c/〈c〉)−b, i.e., P (c) ∼ c−b/〈c〉(1−b) with b ≃ 1. This divergenceat the lowest values of citations also indicate that the Elite journals have a larger proportion of publications with lessnumber of citations although their average number of citations 〈c〉 is larger than those for the general class. However,for both the above classes, the largest citations follow a power law P (c) ∼ c−α, with α ≈ 2.8 ± 0.4 for the General

class and α ≈ 2.7 ± 0.6 for the Elite class, indicating that the mechanism behind the popularity of the very highlycited papers is a ‘rich gets richer’ phenomena [22, 32, 33] (see Fig. 8 of SI for 1980 and 2000). The average numberof papers, total citations and the average number of citations per publication are shown in Table IV and Table V forGeneral and Elite classes. The crossover from the b ≈ 1 in the low citation regime to the P (c) ∼ c−α in the highcitation regime seems to occur around 〈c〉 ≈ 5. We are able to find at least 7 journals (see Fig. 5 and Table V) in theElite class while most of others belong to the General class. To check if this also holds for time-aggregated data, wecollected citations for all papers published during the period 2001-2005 for the same set of journals and repeated theanalysis. We observe that the universality is quite firmly established (see SI. Fig. 9).

C. Measuring inequality

We calculate absolute measures of inequality like the commonly used Gini index [34] as well as the k-index [35, 36]which tells us that the top cited 1− k fraction of papers have k fraction of citations, and we report in Tables. III, IV,V. For academic institutions, Gini index g = 0.7± 0.1 and k = 0.76± 0.04, which means around 76% citations comefrom the top 24% papers. For journals of the General class, g = 0.6±0.2, k = 0.72±0.08, and for journals of the Eliteclass, g = 0.85± 0.10, k = 0.85± 0.05. We also measure the fraction of uncited papers f0. For academic institutions,f0 lies usually in the range 0.1− 0.3, but for journals there are interesting features to be noted. For the General class,f0 is usually around 0.1 or less, but for the Elite class, f0 is consistently larger, ranging from 0.22 − 0.35 in Scienceto 0.46− 0.62 in case of British Medical Journal (BMJ). This is a distinct feature that we found to separate the twoclasses of journals.

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FIG. 5: Probability distribution P (c) of citations c rescaled by average number of citations 〈c〉 to publications from 1990 forseveral academic journals. We separate two major classes of distributions – (A) The General class, whose scaling function fitsto a lognormal function with µ ≈ −0.75, σ ≈ 1.18, while 〈c〉P (c) → const. as c/〈c〉 → 0, and (B) the Elite class for which thescaling function is such that 〈c〉P (c) ∼ (c/〈c〉)−b with b ≃ 1, for the lower range of c. The largest citations fit well to a powerlaw: c−α, with α = 2.8 ± 0.4 for the General class, and α = 2.7± 0.6 for the Elite class.

III. SUMMARY AND CONCLUSION

In this article we present a strong empirical evidence that the citations to science publications from academicinstitutions (universities, research institutes etc.) as well as journals are distributed according to some universalfunction when rescaled by the average number of citations. For institutions, there is an unique universal distribution,most of which fits well to a log-normal function. The largest citations, however, deviate from the lognormal fit, andfollow a power law decay. This universality we claim, is a remarkable feature, since for institutions, the quality of

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scientific output measurable in terms of the total number of publications, total citations etc. vary widely across theworld as well as in time. Nevertheless, the way in which the number of papers with a certain number of citations isdistributed, seems to be quite independent of the quality of production/output of the academic institution. Althoughthere has been claims that the form of the distribution of citations for different scientific disciplines are the same [15],it is also true that each discipline is characterized by a typical average number of citations 〈c〉d. As a matter of fact,that different institutions have a varying strength of publication contribution towards different disciplines makes theissue of obtaining a universal function for the resulting (effective) distribution of citations (for the institution) quitenontrivial. In other words, different academic institutions have a variety in the strength of their academic output, interms of variation of representations across different disciplines and the amount of citations gathered. This does notnecessarily guarantee that the universality which has been already reported across disciplines [15] will still hold whenone looks at data from different institutions, rest aside the counter claims about lack of universal character [30] forcitation distribution across distinct disciplines.However, for journals, the case seems to be a bit different. We do not find an unique distribution of citations, but at

least two classes – a General class, where most of the citations are distributed as log-normal (similar to institutions)and an Elite class, where the universal function decays as 1/c for the low values of citations (Fig. 5). Additionally,we find that a considerably larger fraction of articles are uncited in case of Elite journals compared to the General

class. The tendency of P (c) to diverge at the lowest values of citation comes from the fact that there is a signatureof ‘condensation’ at null citations (c = 0), measured by the fraction of papers with no citations f0, which is quitehigh for the Elite journals. Subsequently, the small values of citations also have a large contribution, contributing tothe divergence 1/c. However, the behavior of the asymptotics (highest citations) is consistent across the classes, thehighest cited papers seem to fit well to a power law decay with a similar exponent (2.7− 3.0). We also note that theElite journals are characterized by high values of impact factors (see Table I) compared to those in the General class,but just having very high impact factors does not ensure the distinctiveness to belong to this league. The presenceof other classes characterized by distinctive nature of their scaling functions is not ruled out. Furthermore, thereare journals specializing in certain disciplines, and also journals which publish articles from different disciplines. Itis quite easy to understand why journals dedicated to a specific subject (e.g. PRA, PRB, etc.) will have the samecharacter, but this will still hold for journals which publish across disciplines (PRL, JAP etc).

Acknowledgments

The authors thank S. Biswas for discussions, J.-I. Inoue, S. Redner and P. Sen for useful comments. A.C. andB.K.C. acknowledges support from B.K.C.’s J. C. Bose Fellowship Research Grant.

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8

Supplementary Information

Data

We collected data from 42 academic institutions across the world. Institutions were selected such that they produceconsiderable amount of papers (typically 200 or more) so that reasonable statistics could be obtained. All paperspublished with at least one author with the institution mentioned as affiliation were collected. This was done for 4years – 1980, 1990, 2000, 2010. We also selected 30 popular academic journals across physics, chemistry, biology andmedicine. However, for some journals, only 3 years of data could be collected, since they were launched after 1980.

TABLE I: Table showing abbreviations used for academic institutions

Abbreviation Full Name of University / Institute

Bern University of BernBHU Banaras Hindu UniversityBordeaux University of BordeauxBoston Boston UniversityBristol University of BristolBuenos Aires University of Buenos AiresCalcutta University of CalcuttaCaltech California Institute of TechnologyCambridge University of CambridgeChicago The University of ChicagoCologne University of CologneColumbia Columbia UniversityDelhi University of DelhiEdinburgh The University of EdinburghGottingen University of GottingenGroningen University of GroningenHarvard Harvard UniversityHeidelberg Heidelberg UniversityHelsinki University of HelsinkiHUJ The Hebrew University of JerusalemIISC Indian Institute of Science

Abbreviation Full Name of University / Institute

Kyoto Kyoto UniversityLandau Inst. Landau Institute for Theoretical PhysicsLeiden Leiden UniversityLeuven University of Leuven – KU LeuvenMadras University of MadrasManchester The University of ManchesterMelbourne The University of MelbourneMIT Massachusetts Institute of TechnologyOsaka Osaka UniversityOslo University of OsloOxford University of OxfordPrinceton Princeton UniversitySINP Saha Institute of Nuclear PhysicsStanford Stanford UniversityStockholm Stockholm UniversityTAU Tel Aviv UniversityTIFR Tata Institute of Fundamental ResearchTokyo The University of TokyoToronto University of TorontoYale Yale UniversityZurich University of Zurich

10-6

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(c)

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CambridgeTokyoOxfordMelbourneHarvardMITTIFRIISCPrincetonDelhiCalcuttaMadras

TAUYaleTorontoKyotoManchesterHUJBernOsloEdinburghBHUGroningenColumbia 10-6

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B2000

2.6

CambridgeTokyoOxfordMelbourneHarvardMITTIFRIISCPrincetonDelhiCalcuttaMadras

TAUYaleTorontoKyotoManchesterHUJBernOsloEdinburghBHUGroningenColumbia

FIG. 6: Probability distribution P (c) of citations c rescaled by average number of citations 〈c〉 to publications from 2 differentyears (1980, 2000) for several academic institutions. Most of the range of the data fit well to a lognormal function withµ ≈ −0.85, σ ≈ 1.32 for 1980 and µ ≈ −0.88, σ ≈ 1.25 for 2000. but the highest citations fit to power laws, with α = 2.5± 0.4for 1980 and α = 2.6± 0.3 for 2000.

9

TABLE II: Table showing abbreviations for journals, and their 2010 Impact factor [37].

Abbreviation Full Name of Journal 2010Impact Factor

Astronomy Astrophys. Astronomy & Astrophysics 4.425Astrophys. J. The Astrophysical Journal 6.063Biochemistry Biochemistry 3.226Eur. J. Biochem./ European Journal of Biochemistry (before 2005) 3.129FEBS Journal FEBS Journal (2005 onwards)Inor. Chem. Inorganic Chemistry 4.326JAP Journal of Applied Physics 2.079J. Chem. Phys. Journal of Chemical Physics 2.921JMMM Journal of Magnetism and Magnetic Materials 1.690J. Org. Chem. Journal of Organic Chemistry 4.002JPA Journal of Physics A: Mathematical and General (before 2007) 1.641

Journal of Physics A: Mathematical and Theoretical (2007 onwards)Langmuir Langmuir 4.269Macromol. Macromolecules 4.838Physica A Physica A 1.522Physica B Physica B 0.856Physica C Physica C 1.415PRA Physical Review A 2.861PRB Physical Review B 3.774PRC Physical Review C 3.416PRD Physical Review D 4.964PRE Physical Review E 2.352PRL Physical Review Letters 7.622Tetrahedron Tetrahedron 3.011

BMJ British Medical Journal 13.471Circulation Circulation 14.432JAMA The Journal of the American Medical Association 30.011Lancet Lancet 33.633Nature Nature 36.104NEJM The New England Journal of Medicine 53.486Science Science 31.377

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(c)

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2001-2005

2.7

CambridgeTokyoHarvardMITIISCTAUKyotoManchesterMelbourneOxfordPrincetonYale

FIG. 7: Probability distribution P (c) of citations c rescaled by average number of citations 〈c〉 to publications from the period2001-2005 for several academic institutions. Most of the range of the data fit well to a lognormal function with µ ≈ −1.1,σ ≈ 1.42. but the highest citations fit to power laws, with α = 2.7± 0.3.

10

TABLE III: Table showing data for number of papers, total number of citations, average citation per paper 〈c〉, Gini (g) index,k index, as well as the fraction of uncited papers f0 from different institutions for several years.

Institutions Year Papers Citations 〈c〉 g k f0Bern 1980 799 12046 15.08 0.771 0.797 0.335

1990 836 23948 28.65 0.713 0.771 0.1452000 1333 44425 33.33 0.658 0.742 0.1422010 2384 34123 14.32 0.686 0.750 0.205

BHU 1980 490 2718 5.55 0.698 0.764 0.2901990 418 3857 9.23 0.706 0.766 0.2162000 387 5276 13.64 0.657 0.746 0.1222010 925 8952 9.68 0.646 0.734 0.145

Boston 1980 899 29898 33.26 0.750 0.787 0.2511990 1450 63769 43.98 0.756 0.787 0.2132000 2431 101914 41.93 0.738 0.777 0.2322010 3798 65091 17.14 0.700 0.759 0.230

Bordeaux 1980 466 7685 16.50 0.713 0.772 0.1891990 710 14410 20.30 0.684 0.755 0.1202000 1198 34600 28.89 0.673 0.750 0.1282010 2171 31841 14.67 0.656 0.741 0.158

Bristol 1980 767 23086 30.10 0.666 0.745 0.1581990 1171 35355 30.20 0.694 0.758 0.1492000 2188 79136 36.17 0.689 0.757 0.1552010 3067 46727 15.24 0.664 0.744 0.176

Buenos Aires 1980 350 3358 9.60 0.871 0.843 0.5231990 551 6960 12.64 0.645 0.738 0.1772000 1269 26297 20.73 0.689 0.754 0.1722010 1853 21009 11.34 0.721 0.766 0.187

Calcutta 1980 162 779 4.81 0.724 0.779 0.2781990 217 1599 7.37 0.634 0.739 0.2262000 173 2252 13.02 0.661 0.743 0.1572010 432 3081 7.14 0.593 0.719 0.163

Caltech 1980 1475 75258 51.03 0.720 0.771 0.1721990 1657 84041 50.72 0.677 0.752 0.0952000 2518 143848 57.13 0.683 0.754 0.1192010 3200 85053 26.58 0.659 0.742 0.096

Cambridge 1980 1676 64474 38.47 0.738 0.779 0.1681990 2605 115593 44.38 0.737 0.779 0.1272000 4885 211330 43.27 0.717 0.769 0.1592010 6454 131833 20.43 0.699 0.759 0.173

Chicago 1980 1852 63709 34.41 0.734 0.779 0.2191990 2096 90196 43.04 0.727 0.775 0.1982000 3080 128711 41.79 0.764 0.789 0.2742010 5077 85669 16.88 0.771 0.791 0.321

Cologne 1980 731 11640 15.93 0.735 0.778 0.2591990 821 20731 25.26 0.725 0.773 0.1332000 1595 43781 27.45 0.698 0.761 0.1942010 2219 28234 12.73 0.684 0.753 0.234

Columbia 1980 1938 73678 38.02 0.736 0.779 0.2041990 2459 121880 49.57 0.705 0.764 0.1482000 3846 180228 46.87 0.729 0.776 0.2192010 6570 114993 17.51 0.708 0.763 0.223

Delhi 1980 425 2694 6.34 0.662 0.747 0.1841990 247 2361 9.56 0.678 0.757 0.1992000 300 4166 13.89 0.683 0.757 0.1542010 914 8277 9.06 0.650 0.738 0.186

Edinburgh 1980 929 26292 28.31 0.770 0.793 0.2021990 1326 42049 31.72 0.699 0.761 0.1592000 2192 87068 39.73 0.702 0.762 0.1662010 3657 70183 19.20 0.706 0.762 0.174

Gottingen 1980 884 13040 14.76 0.696 0.760 0.2131990 1032 38243 37.06 0.815 0.815 0.1262000 1643 51732 31.49 0.689 0.756 0.1392010 2318 36679 15.83 0.683 0.752 0.159

Groningen 1980 636 17173 27.01 0.665 0.746 0.1481990 1061 35353 33.33 0.676 0.750 0.1092000 1811 66440 36.69 0.673 0.747 0.1492010 3835 61010 15.91 0.665 0.743 0.190

Harvard 1980 4891 228195 46.66 0.728 0.775 0.1971990 6011 395808 65.85 0.728 0.775 0.1542000 9539 616902 64.68 0.716 0.770 0.1832010 15139 322575 21.31 0.695 0.759 0.194

Heidelberg 1980 1264 19766 15.64 0.738 0.782 0.2721990 1706 54672 32.05 0.730 0.780 0.1362000 2308 69500 30.12 0.694 0.759 0.1802010 3987 57020 14.31 0.688 0.755 0.245

Helsinki 1980 793 11768 14.84 0.659 0.758 0.1421990 1529 40881 26.74 0.671 0.749 0.1162000 2761 111556 40.41 0.666 0.746 0.1302010 3683 64422 17.50 0.700 0.758 0.164

HUJ 1980 1401 26759 19.10 0.697 0.758 0.2051990 1308 38914 29.76 0.658 0.746 0.0922000 2002 71635 35.79 0.692 0.757 0.1282010 1995 25900 12.99 0.635 0.731 0.154

IISC 1980 447 4827 10.80 0.732 0.778 0.2531990 573 8769 15.31 0.702 0.765 0.1612000 873 21202 24.29 0.669 0.750 0.1122010 1625 14141 8.71 0.619 0.725 0.141

Institutions Year Papers Citations 〈c〉 g k f0Kyoto 1980 2127 46708 21.96 0.685 0.756 0.155

1990 3004 84489 28.13 0.676 0.752 0.1022000 4959 166281 33.54 0.691 0.758 0.1122010 6209 67379 10.86 0.673 0.749 0.208

Landau Inst. 1980 94 5580 59.37 0.808 0.826 0.0431990 104 2621 25.21 0.742 0.794 0.1642000 164 4562 27.82 0.774 0.799 0.0982010 127 1112 8.76 0.619 0.736 0.142

Leiden 1980 737 20627 27.99 0.731 0.773 0.1861990 455 21390 47.02 0.761 0.790 0.1432000 274 10892 39.76 0.701 0.757 0.1172010 562 11574 20.60 0.595 0.715 0.152

Leuven 1980 557 14176 25.46 0.759 0.792 0.2211990 1014 29100 28.70 0.679 0.756 0.1152000 2055 71071 34.59 0.702 0.760 0.1452010 3732 52612 14.10 0.652 0.738 0.163

Madras 1980 193 1342 6.96 0.682 0.760 0.2391990 158 1118 7.08 0.679 0.761 0.2162000 188 2391 12.72 0.631 0.731 0.1602010 349 2895 8.30 0.780 0.796 0.264

Manchester 1980 1256 23178 18.46 0.710 0.767 0.2021990 1644 35766 21.76 0.692 0.758 0.1602000 2475 74563 30.13 0.697 0.760 0.1752010 4495 63993 14.24 0.693 0.756 0.215

Melbourne 1980 863 16322 18.92 0.670 0.751 0.2021990 1131 31257 27.64 0.676 0.751 0.1182000 2112 62221 29.47 0.651 0.741 0.1512010 5268 77387 14.70 0.681 0.750 0.172

MIT 1980 2406 104777 43.55 0.765 0.792 0.2491990 2870 161655 56.33 0.735 0.780 0.1582000 3528 221354 62.75 0.740 0.782 0.1512010 5473 134427 24.57 0.686 0.755 0.147

Osaka 1980 1794 33518 18.69 0.654 0.743 0.1401990 2712 71753 26.46 0.691 0.758 0.1062000 4475 141986 31.73 0.712 0.767 0.1292010 5200 58545 11.26 0.696 0.757 0.224

Oslo 1980 784 17131 21.86 0.675 0.751 0.1621990 835 22227 26.62 0.641 0.737 0.1142000 1471 42358 28.80 0.632 0.731 0.1342010 2966 38633 13.03 0.621 0.726 0.160

Oxford 1980 1240 40022 32.28 0.704 0.766 0.1501990 2136 86263 40.39 0.727 0.777 0.1352000 4061 206346 50.82 0.725 0.771 0.1482010 6876 139360 20.27 0.713 0.765 0.179

Princeton 1980 1048 38529 36.77 0.766 0.792 0.2561990 1117 61433 55.00 0.702 0.764 0.1122000 1727 98350 56.95 0.700 0.761 0.1112010 2229 49765 22.33 0.654 0.741 0.101

SINP 1980 31 174 5.62 0.670 0.745 0.1941990 91 679 7.47 0.640 0.734 0.1322000 148 2466 16.67 0.745 0.778 0.1562010 238 2170 9.12 0.695 0.758 0.181

Stanford 1980 457 20143 44.08 0.858 0.845 0.3551990 364 14578 40.05 0.806 0.816 0.2672000 688 24062 34.98 0.842 0.837 0.3872010 976 12760 13.08 0.844 0.833 0.493

Stockholm 1980 378 10741 28.42 0.688 0.759 0.1381990 615 20564 33.44 0.670 0.754 0.1142000 455 22599 49.67 0.668 0.749 0.0382010 181 4530 25.03 0.761 0.788 0.177

TAU 1980 1141 24247 21.26 0.744 0.781 0.2031990 1516 33531 22.12 0.653 0.740 0.0962000 2532 67183 26.54 0.673 0.749 0.1112010 3433 38481 11.21 0.679 0.752 0.185

TIFR 1980 167 2067 12.38 0.690 0.760 0.1561990 603 10062 16.69 0.729 0.772 0.1552000 439 11585 26.39 0.734 0.773 0.1212010 573 11168 19.50 0.764 0.787 0.135

Tokyo 1980 2869 61636 21.49 0.695 0.760 0.1841990 4196 111101 26.48 0.683 0.756 0.1172000 7945 237735 29.93 0.703 0.763 0.1562010 9191 110392 12.02 0.699 0.760 0.218

Toronto 1980 2345 73405 31.31 0.756 0.786 0.1801990 3210 106541 33.20 0.696 0.761 0.1482000 5187 217357 41.91 0.704 0.765 0.1682010 9240 143557 15.54 0.688 0.755 0.192

Yale 1980 2435 92112 37.83 0.732 0.777 0.2141990 2676 142862 53.39 0.726 0.774 0.1712000 3806 199139 52.33 0.721 0.770 0.2082010 5571 101551 18.23 0.699 0.761 0.226

Zurich 1980 943 15935 16.90 0.786 0.805 0.3321990 879 27736 31.56 0.693 0.760 0.1372000 2238 88817 39.69 0.692 0.760 0.1532010 3860 64315 16.67 0.693 0.754 0.211

11

TABLE IV: Table showing data for number of papers, total number of citations, average citation per paper 〈c〉, Gini (g)index,kindex, as well as the fraction of uncited papers f0 from different journals of the General class for several years.

Journals Year papers citations 〈c〉 g k f0Astronomy 1980 794 21349 26.89 0.629 0.730 0.033Astrophys. 1990 992 28714 28.95 0.575 0.714 0.021

2000 1581 54107 34.23 0.557 0.703 0.0252010 1928 31172 16.17 0.563 0.703 0.040

Astrophys. J 1980 1243 62979 50.67 0.554 0.702 0.0171990 1559 70624 45.31 0.538 0.697 0.0212000 2417 129376 53.53 0.547 0.700 0.0062010 2538 57263 22.57 0.509 0.685 0.017

Biochemistry 1980 951 54432 57.24 0.494 0.677 0.0181990 1653 102958 62.29 0.549 0.697 0.0742000 2022 75696 37.44 0.486 0.672 0.0852010 1161 14141 12.19 0.450 0.658 0.026

Eur. J. 1980 759 35017 46.14 0.549 0.698 0.016Biochem. 1990 790 34665 43.88 0.531 0.692 0.012

2000 852 32230 37.83 0.519 0.684 0.0202010 1524 7129 4.68 0.865 0.852 0.705

Inor. Chem. 1980 856 32225 37.65 0.473 0.670 0.0081990 1111 38417 34.58 0.481 0.673 0.0152000 956 34580 36.18 0.473 0.670 0.0082010 1433 23651 16.51 0.453 0.664 0.017

JAP 1980 1123 33242 29.61 0.669 0.754 0.0571990 2698 55432 20.55 0.651 0.744 0.0852000 2974 75619 25.43 0.612 0.726 0.0332010 3942 29554 7.50 0.510 0.683 0.078

J. Chem. 1980 1931 99340 51.45 0.653 0.740 0.027Phys. 1990 2040 93755 45.96 0.585 0.712 0.021

2000 2598 95409 36.73 0.574 0.708 0.0122010 2209 24241 10.98 0.514 0.684 0.045

JMMM 1980 920 7416 8.07 0.633 0.735 0.1361990 887 9836 11.09 0.688 0.757 0.1462000 837 12209 14.59 0.583 0.713 0.0772010 759 4770 6.29 0.571 0.706 0.134

J. Org. 1980 1379 42032 30.49 0.514 0.686 0.024Chem. 1990 1365 50171 36.76 0.491 0.678 0.015

2000 1428 50152 35.13 0.452 0.662 0.0172010 1214 18759 15.46 0.424 0.652 0.016

JPA 1980 447 10243 22.92 0.762 0.794 0.1281990 737 11085 15.05 0.631 0.737 0.0932000 747 9780 13.10 0.599 0.723 0.0902010 979 5118 5.23 0.585 0.712 0.151

Langmuir 1990 331 14487 43.77 0.585 0.714 0.0252000 1570 72700 46.31 0.528 0.694 0.0042010 2681 40767 15.21 0.456 0.663 0.019

Journals Year papers citations 〈c〉 g k f0Macromol. 1980 335 19969 59.61 0.640 0.735 0.039

1990 934 43934 47.04 0.564 0.708 0.0142000 1388 64747 46.65 0.503 0.683 0.0092010 1386 27925 20.15 0.480 0.671 0.021

Physica A 1980 202 3316 16.42 0.559 0.704 0.0801990 408 6504 15.95 0.657 0.750 0.1262000 631 10032 15.90 0.650 0.743 0.1052010 312 2626 8.42 0.595 0.718 0.167

Physica B 1990 1201 6714 5.60 0.635 0.733 0.1992000 2668 12688 4.76 0.650 0.741 0.2372010 1067 5299 4.97 0.563 0.703 0.169

Physica C 1990 610 16640 27.28 0.588 0.716 0.0202000 1630 8180 5.02 0.664 0.747 0.2492010 903 1987 2.21 0.660 0.743 0.357

PRA 1980 639 25045 39.20 0.613 0.725 0.0361990 1922 55663 28.97 0.607 0.725 0.0442000 1410 40758 28.91 0.611 0.724 0.0272010 2934 30078 10.26 0.527 0.689 0.055

PRB 1980 1413 63380 44.86 0.654 0.745 0.0321990 3487 156697 44.94 0.650 0.741 0.0272000 4814 161122 33.47 0.597 0.719 0.0312010 6207 80554 12.98 0.530 0.692 0.045

PRC 1980 630 19539 31.02 0.655 0.745 0.0351990 728 15594 21.43 0.622 0.730 0.0442000 856 19710 23.03 0.570 0.709 0.0432010 1061 13341 12.58 0.556 0.701 0.058

PRD 1980 800 36764 45.96 0.763 0.797 0.0931990 1049 33816 32.24 0.681 0.760 0.0562000 2059 67840 32.95 0.608 0.726 0.0352010 3012 44349 14.73 0.535 0.694 0.044

PRE 2000 2078 54290 26.13 0.580 0.713 0.0292010 2381 19041 8.00 0.499 0.680 0.070

PRL 1980 1194 89333 74.82 0.664 0.743 0.0481990 1901 160445 84.41 0.637 0.736 0.0282000 3124 234874 75.19 0.590 0.717 0.0122010 3350 85011 25.38 0.512 0.685 0.031

Tetrahedron 1980 403 16248 40.32 0.717 0.774 0.0401990 684 18777 27.46 0.557 0.702 0.0362000 1115 30968 27.78 0.510 0.682 0.0222010 1200 12188 10.16 0.476 0.669 0.033

12

TABLE V: Table showing data for number of papers, total number of citations, average citation per paper 〈c〉, Gini (g)index,kindex, as well as the fraction of uncited papers f0 from different journals of the Elite class for several years.

Journals Year papers citations 〈c〉 g k f0BMJ 1980 3059 27273 8.92 0.886 0.869 0.543

1990 2833 36119 12.75 0.884 0.866 0.4842000 3263 64158 19.67 0.897 0.874 0.4572010 3432 13920 4.06 0.893 0.876 0.619

Circulation 1980 1895 35522 18.75 0.861 0.861 0.3881990 3830 68345 17.85 0.907 0.891 0.4792000 5576 126857 22.76 0.905 0.887 0.6312010 6678 31355 4.70 0.953 0.932 0.877

JAMA 1980 1440 20419 14.18 0.794 0.812 0.3871990 1737 52527 30.25 0.875 0.861 0.4742000 1696 78714 46.42 0.866 0.861 0.3852010 1425 26034 18.27 0.862 0.854 0.460

Lancet 1980 2981 55482 18.62 0.822 0.828 0.3811990 3231 91292 28.26 0.845 0.841 0.3472000 3367 114030 33.87 0.869 0.862 0.3742010 1743 42349 24.30 0.872 0.869 0.403

Nature 1980 2891 181688 62.85 0.799 0.809 0.3381990 3606 318090 88.22 0.857 0.847 0.4352000 2960 446883 150.98 0.810 0.816 0.2922010 2577 121987 47.34 0.786 0.807 0.324

NEJM 1980 1791 76638 42.80 0.858 0.855 0.3801990 1684 118873 70.59 0.854 0.850 0.3492000 1561 142471 91.27 0.874 0.863 0.3442010 1693 64323 38.00 0.858 0.854 0.371

Science 1980 1670 114165 68.37 0.764 0.794 0.2181990 2285 255855 111.98 0.824 0.827 0.3512000 2576 331230 128.59 0.814 0.821 0.2642010 2439 105114 43.10 0.757 0.792 0.266

TABLE VI: Average power law exponents for the highest cited publications for different years (1980, 1990, 2000 and 2010), forInstitutions, All journals, General and Elite journals.

Year Institutions All journals General journals Elite journals1980 2.5± 0.4 2.8± 0.4 2.8± 0.4 2.7± 0.41990 2.6± 0.4 2.8± 0.5 2.8± 0.4 2.7± 0.62000 2.6± 0.3 2.9± 0.3 2.9± 0.3 2.7± 0.32010 2.7± 0.3 3.0± 0.4 3.0± 0.4 3.0± 0.3

13

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10-4

10-3

10-2

10-1

100

101

10-2 10-1 100 101 102

⟨c⟩P

(c)

1980A

2.8

Phys. Rev. Lett.Phys. Rev. APhys. Rev. BPhys. Rev. CPhys. Rev. DJ. Appl. Phys.Astronomy Astrophys.Astrophys. J.J. Chem. Phys.Macromolecues 10-6

10-5

10-4

10-3

10-2

10-1

100

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Phys. Rev. Lett.Phys. Rev. APhys. Rev. BPhys. Rev. CPhys. Rev. DJ. Appl. Phys.Physica BAstronomy Astrophys.Astrophys. J.J. Chem. Phys.LangmuirMacromolecues 10-6

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FIG. 8: Probability distribution P (c) of citations c rescaled by average number of citations 〈c〉 to publications from 2 differentyears (1980, 2000) for several journals of General (left panel) and Elite (right panel) classes. For the General class, the mostof the range fits to a lognormal with µ ≈ −0.69, σ ≈ 1.05 for 1980 and µ ≈ −0.71, σ ≈ 1.12 for 2000. The largest citations forboth the classes do not follow the lognormal behavior, and seem to follow a power law: c−α, with α = 2.8 ± 0.4 for 1980 andα = 2.9± 0.3 for 2000 for the General class, and α = 2.7± 0.4 for 1980 and α = 2.7± 0.3 for 2000 for the Elite class.

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Phys. Rev. Lett.Phys. Rev. APhys. Rev. BPhys. Rev. CPhys. Rev. DJ. Appl. Phys.Physica BAstronomy Astrophys.Astrophys. J.J. Chem. Phys.LangmuirMacromolecues 10-6

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FIG. 9: Probability distribution P (c) of citations c rescaled by average number of citations 〈c〉 to publications from 2001-2005for several journals of General (left panel) and Elite (right panel) classes. For the General class, the most of the range fits to alognormal with µ ≈ −0.71, σ ≈ 1.12. The largest citations for both the classes do not follow the lognormal behavior, and seemto follow a power law: c−α, with α = 2.9 ± 0.2. and α = 2.9± 0.2 for the Elite class.

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FIG. 10: Histograms of power law exponents of the highest cited papers measured from individual data sets, their averagealong with error bar. Data is shown for 4 different years: 1980, 1990, 2000 and 2010, for institutions, all journals, General andElite journals.