**Authors:**Filippo Radicchi, Santo Fortunato, and Claudio Castellano**Publication, Year:**PNAS, 2008- Link to Paper

- The probability that an article is cited $c$ times has large variations between different disciplines
- That being said, all distributions can be represented on a universal curve after rescaling by a relative indicator $c_f = c/c_0$ where $c_0$ is the avg. number of citations per article for that discipline
- i.e. there are large variations of the probability of an article being cited, however, the distributions shape is similar, and can be ovelaid onto one curve across all disciplines - if they are properly rescaled (normalized by the average number of citations)

- This universality is also shown when comparing publications in different years, within the same field
- A
**generalized**is presented as well*h*index- This generalzed
*h*index is built on top of the previous work

- This generalzed

- Citation analysis has a long history and many potential problems have been identified
- Most critical: often a citation does not - nor is it intended to - reflect the scientific quality/relevance of the citied work
- Additional bias
- Self-citations
- Implicity citations
- Increase in total number of citations with time
- Correlation b/w number of authors of an article and the number of citations it receives

- Field variance: the fact that papers in certain fields are cited much more (or much less) than other fields
- This is a large problem with respect to fairly evaluating scientific performance across fields

- Many methods have been proposed to try and alleviate this problem
- Typically, they are based on some sort of normalization step, however, how exactly to do this is contentious
- One option requires the use of
**relative indicators****relative indicators:**ratios between the bare number of citations $c$ and someaverage measure of the citation frequency in the reference field- B/c empircal studies have shown that the number of article citations varies greatly by field, one may wonder whether the use of a simple normalization factor - like the average number of citations - is an appropriate approach.

**Understanding whether this approach is appropriate - with respect to individual publications - is the purpose of this paper**- The normalizing constant used in this paper is:
- $c_0 =$ average number of citations received by all articles in a specific discipline
*for the same year*

- $c_0 =$ average number of citations received by all articles in a specific discipline

- The chance of a publication being cited strongly depends on the field to which it belongs
- E.g. a publication with 100 citations is ~50x more common in Developmental Biology when compared with Aerospace Engineering
- Thus,
*...the simple count of the number of citations is patently misleading to assess whether a article in Developmental Biology is more successful than on in Aerospace Engineering*

- If you scale all citation values across all fields by the average number of citations within that field ($c_f$) and the plot those values - they collapse very nicely to a single line/shape (see below)
- See the original publication if you are curious about the lognormal curve in equation form

- This allows us to confidently declare a universal curve - independent of specific discipline
- See table 1 below for more details on fit quality ($\chi^2$)

- As another test, Radicchi
*et al.*show publication rankings when- ranked by the normal citation count ($c$) and
- ranked after normalizing by $c_f$

- We see that, when ranked after normalization (by $c_f$), each discipline has a relatively equal amount of representation in the ranking.

- The above analysis was done only for the year of 1999. Does it hold with respect to a longitudinal analysis?

- By comparing multiple disciplines across many years we can see evidence of the relative indicators robustness.

- The $h$ index of an author is $h$ if $h$ of his $N$ articles have at least $h$ citations each, and the other $N - h$ articles have, at most, $h$ citations each.
- This measure has adopted spectacular popularity for quantifying the success of academics and has been repurposed for many various purposes.
- See here for some more information on this measure.

- This measure has adopted spectacular popularity for quantifying the success of academics and has been repurposed for many various purposes.
- However, this measure is notoriously limited across disciplines as it is influences by the number of articles that anauthor publishes - which varies between disciplines
- Yet, this variability can also be rescaled away if the number $N$ of publications in a year by an author is divided by the average value of publication in that discipline $N_0$

- This allows for the definition of a
**generalized $h$ index --> $h_f$**- This generalize $h$ index factors out the additional bias due to different publication rates, thus allowing comparisons among scientists working in different fields

- Calculating the $h_f$ index of an author is then found by:
- Ranking the articles by their $c_f$ citations (where $c_f = c/c_0$)
- Rank them from $1\ ...\ n$ where $n =$ the total number of publications
- Note: Pub. with the most citations gets number 1, second most gets 2, and so on increasing by 1 for each publication

- Calculate the
*reduced rank*for each publication- Reduced rank $= r/N_0$
- $r =$ rank
- $N =$ avg. # of publications per own field

- The final generalized $h$ index ($h_f$) = the last
*reduced rank*value such that the corresponding $c_f$ value is larger than the*reduced rank*

$c_f$ | Rank ($r$) | Avg. Pubs. ($N_0$) | Reduced Rank ($r/N_0$) | Keep Going? ($c_f > r/N_0$) |
---|---|---|---|---|

4.1 | 1 | 2 | .5 | Yes |

2.8 | 2 | 2 | 1 | Yes |

2.2 | 3 | 2 | 1.5 | Yes |

1.6 | 4 | 2 | 2 | No |

.8 | 5 | 2 | ||

.4 | 6 | 2 |