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pplication of Bradford’s Law of Scattering to the Physics Literature

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One of the areas in bibliometric research concerns the application of most commonly used bibliometric laws such as Bradford’s Law of Scattering. The paper gives a review of the scholarly contribution on the various facets of Bradford’s Law. In addition to the theoretical aspects of the law, review covers papers dealing with the application of the law in the various subject fields. A study on five-year data of journals (2004-2008) cited by the physicists at the Indian Institute of Science (IISc), Bangaluru was carried out to examine the applicability of Bradford’s Law of Scattering, which include 690 periodicals containing 11,319 references collected from 79 doctoral theses during the period 2004-08.

Ranked list of journals was prepared, and Physical Review-B with 9.53 per cent citation, followed by Physical Review-A with 7.69 per cent, and Astrophysical Journal with 5.47 per cent citations were the most preferred journals. Applicability of Bradford’s Law in various methods was tested. The journal distribution pattern of the IISc doctoral theses does not fit the Bradford’s distribution pattern. The Bradford multipliers were calculated, and the law found to be applicable with the value of k as 1.2. The distribution of the journals in three zones was made and the number of references in each zone was then estimated. The applicability of Leimkuhler model was also tested with the present data. Keywords: Bradford’s law of scattering, Bradford’s multiplier, physics literature, journal citations, core journals, Indian Institute of Science

In every subject there are some journals which are frequently referred by the researchers because of the close relation between the subject of the journals and the areas of research work. These highly cited journals are listed as core journals of the specific subject. The core journals are considered as ‘central set of journals, which most clearly reflects the conceptual essence of the research being reported in the discipline’1. The core journals always contain a higher concentration of relevant articles in a particular discipline. The concept of core journals is derived from Bradford’s Law of Scattering, which was formulated by Samuel Clement Bradford in 1934. Bradford2 first published his observation of the increasing scatter of relevant journal articles on a given topic, and later in 1948, summarised these observations by relating the number of journals in the nuclear, or most productive Received on 12 October 2009 zone, to the number of journals in successively less productive zones containing equal numbers of papers3. Among the several statistical expressions, Bradford’s Law of Scattering is perhaps the most popular and the best known of all the bibliometric concepts that try to describe the effective working of science by mathematical means4.

Bradford’s Law of scattering has been the main topic of many articles in LIS literature. The discussions of the law take several directions: analysis of the law itself, attempts to refine it, comparison with other laws, and its applications. The first notable paper on the law was by Vickery5 and subsequently by Kendall6. The bipolar nature of the law was further discussed by Wilkinson7. He suggested that the verbal formulation expressed Bradford’s theory, while the graphical formulation expressed his observations. The search for an exact formulation of Bradford’s Law was stated by Vickery and Leimkuhler8 and was further pursued by many other authors. In 1977, Brookes9 contributed his theory of Bradford’s law in the commemorative issue of the Journal of Documentation. In this classic paper, Brookes did a complete evaluation of the Bradford’s Law and concluded, “Bradford was therefore a pioneer in social mathematics”. Avramescu10 gave the theoretical foundation of the law.

A comprehensive review of the mathematical evolution of Bradford’s Law was done by Oluic-Vukovic.11 Locket12 reviewed the significant studies. An empirical examination of the Law was done by Qiu13. The gap between empirical and theoretical considerations of the phenomenon described by Bradford’s law has been pointed out by Drott14. Different authors have given many alternative models derived for scattering. Groos15 observed a S-shaped curve (with a droop, at the end of the curve) to explain law of scattering. Fairthorne16 and Asai17 suggested a log model. The dual of Bradford Law was proposed by Egghe18. Burrel19 suggested warring process to explain general features of Bradford’ law. Basu20 suggested that the Bradford’ regularity acquires two pairs of description, Bradford’s verbal law (sequence of ratios) and the classic Leimkuhler law (equation); Bradford’s graphical law (plotted graphs) and Brooke’ law (equation). Again she suggested a model to explain distribution of articles in journals based on probabilistic considerations21. The theory of Bradford Law to the calculation of Leimkuhler Law was proposed by Egghe.22 He also gave a note on different Bradford multipliers.23 To identify a suitable model to explain the law of scattering, Ravichandra Rao24 fitted about 24 different models to the 12 different sets of data. He observed that log-normal model fits much better than many other models, including the log-linear model. Wagner-Dobber25 have also made their comments on the Law. Recently, Nicolaisen and Hjorland26 in their article presented practical potentials of Bradford Law. A number of studies were carried out to verify the authenticity of the Bradford’s law. On the application side, the studies of Sengupta,27 and Goffman and Morris28 are significant. The applicability of the two vital formulations (verbal and graphical) of Bradford’s law of Scattering was tested by Arjun Lal and Panda29. The data were collected from 20 doctoral theses in plant Pathology submitted to Rajendra Agricultural University, Bihar, during 1980-93. Gupta30 studied the applicability of Bradford’s law to citation data in Ethiopian Medical Journal. Other studies include, Lawani31 in Agriculture, Tyagi32 in Physics, Nweke33 in Zoology, Asundi and Kabir34 in Horticulture, Bandyopadhyay35 in different disciplines, Sukla and Saksena36 in Bioenergy,
and 4

Gupta and Suresh Kumar37 in theoretical population genetics. The Law has been applied to study not only the scattering of publications, but in other sphere of activities also. A study conducted by Garg and Lalitha Sharma38 of R&D indicators in Indian industry using Bradford’s Law bears testimony to this fact. Many scholars have studied the application of Bradford’s Law in the distribution of publications in journals, coverage in international indexing and abstracting services, etc., but few have analysed the applicability of Bradford’s Law in the distribution of journal citations in a particular institution. Hence, this study on the journals cited by the physicist of IISc in their doctoral theses becomes significant. IISc is the premier S&T research institute in the country, where research in all the major areas of physics is being carried out. IISc celebrated its centenary in 2008.

The main objectives of the study were: (i) To prepare a rank list of most cited journals by the IISc physicists.

(ii) To study the phenomenon of scattering for citation data. (iii) To test the appropriateness of verbal and graphical formulation of Bradford’s Law of Scattering.

A total of 690 journals containing 11,319 references collected from 79 doctoral theses were arranged in descending order of productivity. The study treated references as items and journals as sources. The verbal formulation was tested by three separate parameters for carrying the different number of periodicals, while for testing the appropriateness of graphical formulation, the natural log value of the cumulative number of journals was calculated for plotting the graph.

4.1 Bradford’s Law of Scattering
Bradford’s Law of Scattering describes a quantitative relation between
journals and the papers these publish. Samuel Clement Bradford, Chief Librarian at the London Science Museum, made statistical analysis of two geophysics bibliographies, the Current Bibliography of Applied Geophysics (1928-1931) and the Quarterly Bibliography of Lubrication (1931-1933)2. He tested the journals containing references to these fields in their descending order of productivity and then divided the articles into three approximately equal zones or groups. He termed the first one as the nuclear zone, which is highly productive; the second zone as moderately productive zone; and the third zone as peripheral zone or low productive zone. Bradford discovered regularity in DESIDOC Jl. Lib. Inf. Technol., 2010, 30(2)

calculating the number of titles in each of the three zones. On the basis of the observations, Bradford concluded that the ratio of the titles of journals in successive zones followed a common pattern. Bradford’s verbal formulation stated that if scientific journals are arranged in order of their decreasing productivity of articles on a given subject, they may be divided into a nucleus of periodicals more particularly devoted to the subject, and several ‘groups’ or ‘zones’ containing the same number of articles as the nucleus, where the number of periodicals in the nucleus and succeeding zones will be 1: n: n2, where ‘n’ is a multiplier3. Based on Bradford’s observations, Brookes39 suggested the following linear relation to describe the scattering phenomenon as: F(x) = a + b log x where F(x) is the cumulative number of references contained in the first x most productive journals, and a and b are constants. This is the most widely used formulation of Bradford’s Law. Vickery extended the verbal formulation to show that it can be applied to any number of zones of equal yield. Leimkuhler8 issued the following simple function for Bradford’ distribution, which was named after him: R(r) = a log ( 1 + br) where R (r) is the cumulative number of articles contributed by journals ranked 1 through r, and a and b are parameters. Similarly, Brookes derivation for journal productivity takes the form R (r) = a log (b/r) Further, Wilkinson7 noticed that the formulae provided by Leimkuhler and Brookes did not really describe the same phenomenon. Starting from the late 1960s, several mathematical formulations, models, and syntheses of previous statements related to Bradford’s Law have been put forth, but very little agreement exists about
which model is the best. Brookes expression of the Bradford distribution has however gained wide acceptance.

of the articles, to be followed by a second larger group of journals that accounts for another third, while a much larger group of journals picked up the last third3. There are two most widely recognised formulations of the so called Bradford’s Law: the verbal formulation which is derived from the verbal statement of Bradford’s conclusion, and the graphical formulation, which is an empirical expression derived from the graphical survey of a distribution of periodicals40. Bradford did not give a mathematical model for his law. Models were suggested later by Brookes, Vickery and Leimkuhler. Several authors, while explaining the scattering of articles in journals, have formulated many different models of Bradford’s Law. Leimkuhler developed a model based on Bradford’s verbal formulation as41: R (r) = a log (1+br) r = 1, 2, 3 … while explaining Leimkuhler’s Law, Egghe shows that a = Y0/log k b = k-1/r0 (2) (3) (1)

where r0 is the number of sources in the first Bradford group, Y0 the number of items in every Bradford group (all these group of item being of equal sizes), and k the Bradford multiplier. R(r) is the cumulative number of items produced by the sources of rank 1, 2, 3…r and a and b are constants appearing in the law of Leimkuhler. In forming Bradford groups, it is shown that the number of groups p is a parameter that can be chosen freely. Egghe22 has shown the mathematical formula for calculating the Bradford Multiplier k as k = (eγ ym) 1/p where g is Euler’s number (eg = 1.781). If the sources are ranked in decreasing order of productivity, then ym is the number of items in the most productivity sources. Then y0 and r0 are: Y0 = y2m log k and r0 = (k-1)Ym (5) (6) (4)

4.2 Theoretical Aspects of Bradford’s Law
Bradford’s Law of Scattering describes a quantitative relationship between journals and the papers they publish. It explains that, only a small number of core journals will supply the nucleus of papers on a given topic which accounts for a substantial percentage (1/3) DESIDOC Jl. Lib. Inf. Technol., 2010, 30(2)

Once p is chosen, the value of k can be calculated by using

k = (1.781 ym) 1/p and Y0 = A/P where A denotes the total number of articles.


than newer journals. Majority of the most cited journals of IISc are being published for about or more than 100 years. Physical Review B (110 Years), Physical Review A (110 Years), Astrophysical Journal (108 Years), Nature (134 Years), etc. Among the journals listed in the Table 1, some journals include the word ‘letters’ or ‘communication’ in their titles. These journals are letters or communication type, such as Physical review Letters, Applied Physics Letters, Solid State Communication, Physics Review letters etc. The purpose of this preliminary communication is to establish priority for an invention and to disseminate nascent information on current research in the scientific community. Nature and Science, though they are not letters journals, their main purpose is reporting preliminary communication and current research. In general, these journals publish short articles with a short time interval and most of them are weekly or biweekly publications. With more new information to be cited, it is not surprising that these journals are receiving more citations than the general journals, as seen in the IISc ranked journal list43. The next remarkable feature of the study is the high status of multi-disciplinary science journals in the core journals list of Physics literature. It is evident from the analysis that Nature, Current Science, Science, Proc. Indian Academy of Science, Proc. Nati. Acad.; Sci. Proc. Roy. Soc. London, etc. are in the top ranks in IISc theses. The top ranked journals of IISc researchers indicate that 8 out of the first 10 journals are published from USA. It is also interesting to see that out of the top 10 journals, 4 journals are published by American Institute of Physics (AIP) and 3 journals are by American Physical Society (APS). The prestigious science journal Nature published by the Nature publishing group of United Kingdom is in the 9th position with 223 (1.95 per cent) citations.

Let T denote the total number of journals in Bradford group, there are r0k i-1 sources (i = 1, 2, 3……p) T = r0 + r0k + r0k2 +………+ r0kp-2 (8)

So, r0 = T/1+k+k2+…………+kp-1 = T(k-1)/(kp-1) (9) Since A and T are known from the data set, r0 and Y0 are calculated, once p is calculated by the formula (7) Gupta and Suresh Kumar37 have given the theoretical aspects of Bradford’s Law and studied its applicability using the above method. According to Brookes42, to test the conformity of Bradford’s law, one should meet the following three implicit conditions: (i) In dividing the journals into zones, the number of articles in each zone must remain constant.

(ii) The Bradford multiplier k must be >1. (iii) The Bradford multiplier must remain approximately constant.

5. ANALYSIS AND DISCUSSION 5.1 Top-ranked Journals
Core journals ranking studies are usually made to help in the selection of journals and in assessing the importance of one or more journals in a particular subject field. The journals are arranged in their respective descending order of frequency and in alphabetical order among the same rank number. The journal contributing the largest number of articles is ranked as number one, next is ranked two and so on. The criterion for ranking is purely quantitative not qualitative. The ranked list of most cited journals of IISc are shown in the Table 1. In the analysis, the citation of articles is distributed in 690 journals with a total of 11,412 citations. From the Table 1 it is clear that Physical Review B, a specialised journal in the area of Condensed Matter Physics published by American Physical Society (APS) tops the list with the highest contribution of 1087 (9.53 per cent) citations. Physical Review A, also a publication of APS, is in the second position by accounting 878 (7.69 per cent) articles, while Astrophysical Journal, published from USA by University of Chicago Press occupies the third position with 624 (5.47 per cent) citations. Of the journals of IISc, 51 journals are cited at least 37 times or more. The most cited journals are usually well established and known worldwide. With more available to be cited more often 6

5.2 Application of Bradford’ Law
To observe the appropriateness of the distribution of journals using the verbal formulation of Bradford Law, the following explanations are made and the results presented. The first part deals with the verbal formulation of the theory based on data consisting whole periodical references, arranged by their decreasing frequency of citations while the second part examines the graphical representations based on the same data.

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