Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## tapered *h-*index

*h-*index, while also giving every citation some small influence on the score.
### History

## References

While the rational *h-*index gives a fractional value to those citations necessary to reach the next value of *h,* the tapered *h-*index (Anderson *et al.* 2008) is designed to give every citation for every publication some fractional value. The best way to understand this index is to first consider the contribution of every citation to the *h-*index. To have an *h-*index of 1, an author needs a single paper with a single citation. That citation has a weight (or score) of 1, because it accounts for the entire *h* value of 1. To move to an *h-*index of 2, the author needs three additional citations: one additional citation for the original publication and two citations for a second publication. As *h* has increased by one, each of these three citations is contributing a weight (or score) of 1/3 to the total *h-*index. This is most easily illustrated by a Ferrers graph of ranked publications versus citations which shows the specific contribution of every citation to a specific value of *h*

Citation | ||||||||
---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | → | ||

Ranked publication | 1 | 1 | 1/3 | 1/5 | 1/7 | 1/9 | 1/11 | |

2 | 1/3 | 1/3 | 1/5 | 1/7 | ||||

3 | 1/5 | 1/5 | 1/5 | 1/7 | ||||

4 | 1/7 | 1/7 | ||||||

5 | 1/9 | |||||||

↓ |

The largest filled-in square in the upper left corner (the Durfee square) has a length equal to *h;* the contents of the square also sum to *h.* Using this logic, one can determine the credit each citation would give to a larger value of *h,* regardless of whether that *h* has been reached. Consider this graph with respect to the rational *h-*index. In the above example, *h* is 3. If one just considers the citations necessary to reach an *h* of 4, we can see that 5 of the 7 necessary citations are already present. Each of these has a weight of 1/7 (since 7 total citations are necessary); adding these to *h* we get the rational *h-*index, \(h^\Delta=3.71\). The tapered *h-*index is simply taking this same concept but expanding it to include all citations for all publications.

The tapered *h-*index for a specific publication is the sum of all of its scores and the total score of the index is the sum across all publications. In simple formulaic terms, the score *h _{T}*(

and the total tapered *h-*index is the sum of these scores for all publications,

Year | h_{T} |
---|---|

1997 | 1.3333 |

1998 | 3.7437 |

1999 | 4.8642 |

2000 | 7.4899 |

2001 | 9.6576 |

2002 | 12.3077 |

2003 | 15.0441 |

2004 | 18.5548 |

2005 | 21.1995 |

2006 | 23.7368 |

2007 | 26.8198 |

2008 | 29.0324 |

2009 | 32.1712 |

2010 | 35.5884 |

2011 | 38.2048 |

2012 | 40.0496 |

2013 | 43.0222 |

2014 | 44.6786 |

2015 | 46.8178 |

2016 | 47.5942 |

2017 | 48.3933 |

- Anderson, T.R., R.K.S. Hankin, and P.D. Killworth (2008) Beyond the Durfee square: Enhancing the
*h-*index to score total publication output.*Scientometrics*76(3):577–588.