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Theory of Citing

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Book cover Handbook of Optimization in Complex Networks

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 57))

Abstract

We present empirical data on misprints in citations to 12 high-profile papers. The great majority of misprints are identical to misprints in articles that earlier cited the same paper. The distribution of the numbers of misprint repetitions follows a power law. We develop a stochastic model of the citation process, which explains these findings and shows that about 70–90% of scientific citations are copied from the lists of references used in other papers. Citation copying can explain not only why some misprints become popular, but also why some papers become highly cited. We show that a model where a scientist picks few random papers, cites them, and copies a fraction of their references accounts quantitatively for empirically observed distribution of citations.

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Notes

  1. 1.

    See, for example, the discussion “Scientists Don’t Read the Papers They Cite” on Slashdot: http://science.slashdot.org/article.pl?sid=02/12/14/0115243&mode=thread&tid=134.

  2. 2.

    Suppose that the number of occurrences of a misprint (K), as a function of the rank (r), when the rank is determined by the above frequency of occurrence (so that the most popular misprint has rank 1, second most frequent misprint has rank 2 and so on), follows a Zipf law: K(r) = C ∕ r α. We want to find the number-frequency distribution, i.e. how many misprints appeared n times. The number of misprints that appeared between K 1 and K 2 times is obviously r 2 − r 1,  where K 1 = C ∕ r 1 α and K 2 = C ∕ r 2 α. Therefore, the number of misprints that appeared K times, N k , satisfies N K dK =  − dr and hence, N K  =  − dr ∕ dK ∼ K  − 1 ∕ α − 1.

  3. 3.

    Why did this happen? Obviously, T reaches maximum when R equals zero. Substituting R = 0 in (16.22) we get: T MAX = N(1 − 1 ∕ N M). For paper No.4 we have N = 2, 578, M = D ∕ N = 32 ∕ 2, 578. Substituting this into the preceding equation, we get T MAX = 239. The observed value T = 263 is therefore higher than an expectation value of T for any R. This does not immediately suggest discrepancy between the model and experiment but a strong fluctuation. In fact out of 1,000,000 runs of Monte Carlo simulation of MPM with the parameters of the mentioned paper and R = 0. 2 exactly 49,712 runs (almost 5%) produced T ≥ 263.

  4. 4.

    There are also misprints where author, journal, volume, and year are perfectly correct, but the page number is totally different. Probably, in such case the citer mistakenly took the page number from a neighboring paper in the reference list he was lifting the citation from.

  5. 5.

    In our initial report [22] we mentioned “over 24 thousand papers.” This number is incorrect and the reader surely understands the reason: misprints. In fact, out of 24,295 “papers” in that dataset only 18,560 turned out to be real papers and 5,735 “papers” turned out to be misprinted citations. These “papers” got 17,382 out of 351,868 citations. That is every distinct misprint on average appeared three times. As one could expect, cleaning out misprints lead to much better agreement between experiment and theory: compare Fig.16.8 and Fig. 1 of [22].

  6. 6.

    If one assumes that all papers are created equal then the probability to win m out of n possible citations when the total number of cited papers is N is given by the Poisson distribution: P = ((n ∕ N)m ∕ m! ) ×e  − n ∕ N. Using Stirling’s formula one can rewrite this as: ln(P) ⊈m ln(ne ∕ Nm) − (n ∕ N). After substituting n = 330, 000, m = 500 and N = 18500 into the above equation we get: ln(P) ⊈ − 1, 180, or P⊈ 10 − 512.

  7. 7.

    Sociologist of science Robert Merton observed [19] that when a scientist gets recognition early in his career he is likely to get more and more recognition. He called it “Matthew Effect” because in Gospel according to Mathew (25:29) appear the words: “unto every one that hath shall be given”. The attribution of a special role to St. Matthew is unfair. The quoted words belong to Jesus and also appear in Luke and Mark’s gospels. Nevertheless, thousands of people who did not read The Bible copied the name “Matthew Effect.”

  8. 8.

    From the mathematical perspective, almost identical to RCS model (the only difference was that they considered an undirected graph, while citation graph is directed) was earlier proposed in [23].

  9. 9.

    The analysis presented here also applies to a more general case when m is not a constant, but a random variable. In that case m in all of the equations that follow should be interpreted as the mean value of this variable.

  10. 10.

    Some of these references do not deal with citing, but with other social processes, which are modeled using the same mathematical tools. Here we rephrase the results of such papers in terms of citations for simplicity.

  11. 11.

    The uncertainty in the value of α depends not only on the accuracy of the estimate of the fraction of citations which goes to previous year papers. We also arbitrarily defined recent paper (in the sense of our model), as the one published within a year. Of course, this is by order of magnitude correct, but the true value can be anywhere between half a year and 2 years.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of California, Los Angeles, CA, 90095-1594, USA

    M. V. Simkin & V. P. Roychowdhury

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  1. M. V. Simkin
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  2. V. P. Roychowdhury
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Correspondence to M. V. Simkin .

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Editors and Affiliations

  1. Science and Engineering, Department of Computer and Information, University of Florida, Gainesville, 3260, Florida, USA

    My T. Thai

  2. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611-6595, Florida, USA

    Panos M. Pardalos

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Simkin, M.V., Roychowdhury, V.P. (2012). Theory of Citing. In: Thai, M., Pardalos, P. (eds) Handbook of Optimization in Complex Networks. Springer Optimization and Its Applications(), vol 57. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0754-6_16

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