Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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*q-*index

### Example

### History

## References

The *q-*index (Bartneck and Kokkelmans 2011) is an attempt to measure whether an author is manipulating their own *h-*index through self-citation. It calculates a potential cost of a self-citation for each publication whose citation count is equal or less than *h,* sums these costs for all self-citations, then normalizes by the total number of publications. Essentially, publications with a citation count equal to *h* generate a cost of 1 per self-citation, with each subsequent publication in rank order generating costs of 1/2, 1/3, 1/4, etc., with ties generating equal values. The potential costs are calculated as:

where

$$a_i=\left|\begin{matrix} 0 & \text{if }i \leq h \\ a_{i-1} & \text{if }i>h \text{ and } C_i \neq C_{i-1}\\ 1+a_{i-1} & \text{if }i>h \text{ and } C_i = C_{i-1} \end{matrix}\right. .$$The total self-citations for any publication where *C _{i}* ≤

where *c _{i}* is the number of self-citations to the

Simulations indicate that selective citing to boost *h* may lead to a *q*-index, greater than one, while lower values are found when self-citation is random or fair.

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 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Self Citations (c)_{i} | 1 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |

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

h = 6 | ||||||||||||||||

a_{i} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 2 | 3 | 4 | 4 | 5 | 6 |

q_{i} | 0 | 0 | 0 | 0 | 0 | 0 | 1/2 | 1/3 | 1/3 | 1/3 | 1/4 | 1/4 | 1/4 | 1/5 | 1/5 | 1/5 |

c_{i}q_{i} | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.667 | 0.000 | 0.000 | 0.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

The sum of *c _{i}q_{i}* is 1.9167, thus Q is 0.1198.

Year | Q |
---|---|

1997 | 0.4000 |

1998 | 0.0556 |

1999 | 0.1190 |

2000 | 0.2500 |

2001 | 0.1198 |

2002 | 0.1443 |

2003 | 0.2854 |

2004 | 0.1651 |

2005 | 0.2070 |

2006 | 0.2630 |

2007 | 0.2200 |

2008 | 0.1843 |

2009 | 0.1772 |

2010 | 0.1185 |

2011 | 0.1739 |

2012 | 0.0968 |

2013 | 0.0671 |

2014 | 0.0611 |

2015 | 0.0425 |

2016 | 0.1414 |

2017 | 0.1385 |

- Bartneck, C., and S. Kokkelmans (2011) Detecting
*h-*index manipulation through self-citation analysis.*Scientometrics*87(1):85–98.