Computational Evolutionary Biology & Bioinformatics

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*w-*index (Woeginger)

### Example

### History

## References

Woeginger's *w-*index (Woeginger 2008) is somewhat similar to the *h-*index. It is the largest value of *w* for which publications have at least 1, 2, 3, …*w* citations:

for all *i* ≤ *k*. Put another way, the top 1…*k* publications have to have at least *k*…1 citations, respectively.

Graphically, if the *h-*index is the largest square with sides *h* that can fit under the citation curve, *w* is the largest right-angled isoceles triangle with perpendicular sides of *w*.

Publications are ordered by number of citations, from highest to lowest.

Citations (C)_{i} | 42 | 36 | 14 | 11 | 9 | 9 | 3 | 2 | 2 | 2 | 1 | 1 | 1 | 0 | 0 | 0 | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Rank (k) | k…1 | |||||||||||||||||

1 | 1 | |||||||||||||||||

2 | 2 | 1 | ||||||||||||||||

3 | 3 | 2 | 1 | |||||||||||||||

4 | 4 | 3 | 2 | 1 | ||||||||||||||

5 | 5 | 4 | 3 | 2 | 1 | |||||||||||||

6 | 6 | 5 | 4 | 3 | 2 | 1 | ||||||||||||

7 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | |||||||||||

8 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | ||||||||||

w = 9 | 9 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | ||||||||

10 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | ||||||||

11 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | |||||||

12 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | ||||||

13 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | |||||

14 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | ||||

15 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | |||

16 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |

The largest rank where the minimum number of citations for publications 1…*k* ≤ *k*…1 is 9.

Year | w |
---|---|

1997 | 1 |

1998 | 4 |

1999 | 5 |

2000 | 8 |

2001 | 9 |

2002 | 13 |

2003 | 17 |

2004 | 22 |

2005 | 25 |

2006 | 29 |

2007 | 32 |

2008 | 35 |

2009 | 35 |

2010 | 40 |

2011 | 42 |

2012 | 44 |

2013 | 45 |

2014 | 46 |

2015 | 47 |

2016 | 49 |

2017 | 49 |

- Woeginger, G.J. (2008) An axiomatic characterization of the Hirsch-index.
*Mathematical Social Sciences*56(2):224–242.