An Interactive Citation Simulator

In my last post on citation rates, I described the output of a citation simulator, and I promised an interactive version. As it turns out, creating computation-heavy JavaScript that doesn’t completely bog down browsers is hard; hence the delay in posting.1 But here it is!

I’ve added a few presets that illustrate the phenomena I talked about in my last post. The order-of-magnitude changes I talked about overwhelm even Chrome’s JavaScript engine, but these somewhat smaller changes show similar behavior.2

  • The default has all settings at their lowest value except for the number of journals (100), the bias (1), and the decay (75 percent). Lower the number of journals to 50 if the simulator runs too slowly; the results are similar, though somewhat inflated.

  • The first preset has the same settings as the default, but increases the number of outgoing citations per article to 40.

  • The second preset has the same settings as the default, but increases the number of issues per year per journal to 20.

If you run the simulator on these three presets, you’ll see that increasing the number of issues per year produces a 100 percent jump in the top H5 index. Increasing the number of outgoing citations per article produces a 35 percent jump. If you combine both increases, there’s a 250 percent jump; these two settings are mutually reinforcing. But the relative effect of increasing journal output is still stronger, as you can see if you hold the number of outgoing citations at 40 and increase the number of issues per year from 5 to 20.

I’ve also included three additional presets that illustrate the effect of the bias parameter.

  • The third preset has the same settings as the default, but reduces the bias term to 0, and reduces the decay term to 25 percent.
  • The fourth preset has the same settings as preset three, but increases the number of outgoing citations per article to 40.

  • The fifth preset has the same settings as preset three, but increases the number of issues per year per journal to 20.

These three presets show that the relative impact of the outgoing citations and issues per year parameters depends highly on the bias parameter. Because the bias is 0, every active article is equally likely to be cited.3 Under these circumstances, increasing the number of outgoing citations produces a much larger jump in H5 indices.

Please play with this and let me know if you run into any problems!

DefaultPreset 1Preset 2Preset 3Preset 4Preset 5

Number of Journals: 
Outgoing Citations Per Article: 
Articles Per Issue: 
Issues Per Year: 
H-Index: 
Bias Exponent: 
Decay Probability: 

StepRunStopReset

Current year:
Average H5 score for top journal:
Average H5 score for median journal:

Top H Scores:

Maximum incoming citations per article within each decile of active articles (log scale):


  1. I clearly need to learn about web workers, because this still bogs down the page on high settings; use with caution! 
  2. The values jump around a little at the beginning; this is because of "edge effects" early in the simulation. After the first eight or ten years, the values often stabilize -- but for some settings they continue to jump around in a way that suggests chaotic behavior. In most cases, the averages tend to converge to a stable point after about thirty years. 
  3. The exponential decay you see in the second chart is due to the decay term, which steadily removes papers from the pool of citable papers. Since older papers are both more likely to be highly cited and more likely to be removed from the pool, most papers are cited only a few times. 

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