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I wonder if the following bibliometric index exists. If a paper cites n other papers, then give a weight of 1/n to each. Then one can sum up these weights for each paper/person to get an index.

This would balances things in the sense that in some fields papers cite 5 other papers, while in other fields 100 - so scientists of the two fields can be better compared. It would be especially useful when someone works in two different fields, like (you would never guess!) myself - among mathematicians, my citations overrate me, but among theoretical computer scientists I'm nowhere.

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    But why should citing more papers be a negative factor for each of them? – BioGeo Dec 2 '16 at 12:35
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    @BioGeo: It is not necessarily a negative factor, but as we know all too well, there is no perfect bibliometric. My proposal aims to balance the fact that some fields have more citations in general. – domotorp Dec 2 '16 at 13:30
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If I understand you correctly, you are referring to a concept called citing-side normalization (see e.g. Waltman & vanEck 2013), where the number of references of citing papers are used as weighting factors to account for the different lenghts of reference lists in different fields (citation density). This type of normalization is relatively common within bibliometrics, so I think that the other answers are incorrect in saying that they don't exist. One well-known example of such an index is the SNIP-indicator (see Waltman et al., 2013 and Leydesdorff & Opthof, 2010), which is a journal-level indicator. Another example is the recently proposed article-level CSNCR-index (citation score normalized by cited references, see Bornmann & Haunschild, 2016), but this uses the mean number of cited references in a field to normalize citations (so not references list length in individual papers).

If you look for references to "citing-side normalization" you will find other examples of similar approaches, at journal or article levels. I'm not sure if I've seen author-level indices based on this though (but averages of article-level indicies can of course be used). In general, there are a number of bibliometric indices that control for the different citations densities in different fields (not only using citing-side normalization). These are all based on some sort of field normalization, which can be done for field classes (in e.g. Scopus or Web of Science) or other article groupings (see e.g. the cluster-based normalization used at CWTS in Leiden).

  • Yes, exactly what I was looking for! Are their places online where one can look these statistics up? – domotorp Dec 20 '16 at 10:11
  • @domotorp Journal-level metrics (eg SNIP) can be found at both Scopus (journalmetrics.scopus.com) and WoS. I don't think that article-level indices are publically avaliable, but many organizations calculate them in different forms for evaluation purposes (e.g. at CWTS, or where I'm currently working). The basic idea then is that the number of citations to papers are normalized by the number of citations in their field, but methods differ on how these fields reference values are defined. In the simplest case, the number of citations to a paper is divided by the field average. – fileunderwater Dec 20 '16 at 10:19
  • [cnt...] In this case, field normalized values above one indicate that the paper is cited more than the average paper and a value below one indicate that it is cited less than the average paper. Methods then differ on how to define fields, or how to calculate reference values (mean, median, decentiles etc). – fileunderwater Dec 20 '16 at 10:34
  • I would be more interested in person-level metrics, as I've explained in the motivation. – domotorp Dec 20 '16 at 11:48
  • @domotorp I sort of suspected that ;) Unfortunately, from what I know, there is no publically available version. WoS and Scopus could certainly show them, but has chosen to only make them available through their extra services (against a fee). So if you have access to e.g. Thomson-reuters/Clarivate's 'Essential Science Indicators' you can get some versions of filed normalizations. Other organizations have local copies of WoS or Scopus and can therefore perform different kinds of field normalizations. – fileunderwater Dec 20 '16 at 19:32
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As far as I know, no such bibliometric is in use. However, I think your question is predicated on a couple of misconceptions, which I will try to clear up.

  • First, your citation count doesn't "rate" you as a researcher. Yes, it's something that people often look at in context with other things to get an idea of how much an impact your research has, but any bibliometric only captures a small aspect of this (if you want, you can think of this as a random variable which measures "impact" or "influence, but with extremely large variance). And people know average citation counts vary a lot by fields and subfields. Serious researchers in your field will evaluate you based on your work and the opinion of experts in the field.

I don't think your idea is a bad one, but there are also various issues with the bibliometric you propose, which you may or may not have thought about:

  • One obvious drawback is that this number no longer measures "scope of impact." One person who writes a paper with a single citation, which is only a self-cite (e.g., this may happen in a corrigendum) gets a 1 for this bibliometric, which is the same value as someone who in 20 different papers with 20 references each.

  • The number of references a paper has is largely a function of the authors' style and type of paper being written.

  • When authors add gratuitous self-cites or pressure others to cite their works, that unfairly lowers this bibliometric for the other references.

  • Also, you might philsophically be thinking of the weight in your proposed bibliometric as a measure of how much a cited paper influenced the current one, but the reality is far different. Some cited papers will be a lot more influential than other ones for a given work, and there is no simple bibliometric way to determine (cf. https://academia.stackexchange.com/a/62917/19607).

  • Not a drawback so much as pushback: this will give everyone a smaller citation number than they currently have, so I can imagine many people would be against it.

  • I agree with everything that you wrote, I didn't have any of these misconceptions. What I claim is simply that this index has some advantages over the simple citation count, and I don't see any disadvantages (compared to simple citation count). – domotorp Dec 2 '16 at 17:10
  • @domotorp Oh, good. Based on the question, I thought you might have misconceptions at least about the first bullet point. I'll add a couple of things what I see as drawbacks. – Kimball Dec 2 '16 at 17:22
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    @domotorp: "I don't see any disadvantages (compared to simple citation count)" - let me repeat the disadvantage I already mentioned in the first version of your question earlier today that you have deleted meanwhile: In the CS subfields I am most acquainted with, low-quality and workshop papers are likely to have rather few references (< 10), whereas top-tier conference papers typically have rather many references (30 - 50). With simple citation count, each citation has the same weight, so citations by low-quality publications unduly increase the aggregate value. With your model, citations ... – O. R. Mapper Dec 2 '16 at 19:31
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    ... by low-quality publications are likely to weigh more than citations in better publications, so the distortion is made worse. – O. R. Mapper Dec 2 '16 at 19:32
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    @domotorp... at which point, the effect of being mentioned in a comprehensive review paper will drown out all other citation effects. – Andrew Dec 4 '16 at 10:53
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Currently, there is no standard bibliometric that fits your definition. This could be mainly due to the complexity (and biases) involved.

Your bibliometric proposal looks analogous to the PageRank algorithm. Only that you cannot directly apply it since citation graphs are DAGs by nature. There is a paper that shows how to apply weighted PageRank to author citation networks that you might want to read.

  • Also this one by some colleagues of mine: A combined approach for evaluating papers, authors and scientific journals sciencedirect.com/science/article/pii/S0377042710000749 – Federico Poloni Dec 2 '16 at 13:10
  • I don't think these are similar because mine doesn't involve any recursion or any complicated computation - every person can easily count their own index by looking at the citation list of all the papers citing their work. – domotorp Dec 2 '16 at 13:28
  • @domotorp Well in that case, it would be simple enough to code it yourself. – Ébe Isaac Dec 2 '16 at 13:31
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    Rather, citation graphs are close to being DAGs. – Tobias Kildetoft Dec 2 '16 at 13:35
  • Unfortunately, I don't code. Also, just because I'm curious about something, it doesn't necessarily mean that I want to spend several days making a program that outputs the answer. Which, or course, would be meaningless without comparison to other people's numbers. – domotorp Dec 2 '16 at 13:52

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