Scientific indexes

H-index

The h-index is an index that attempts to measure both the scientific productivity and the apparent scientific impact of a scientist. The index is based on the set of the scientist's most cited papers and the number of citations that they have received in other people's publications. The index can also be applied to the productivity and impact of a group of scientists, such as a department or university or country. The index was suggested by Jorge E. Hirsch, a physicist at UCSD, as a tool for determining theoretical physicists' relative quality and is sometimes called the Hirsch index or Hirsch number.
The index is based on the distribution of citations received by a given researcher's publications.

Hirsch writes:

A scientist has index h if h of [his/her] Np papers have at least h citations each, and the other (Np − h) papers have at most h citations each.
In other words, a scholar with an index of h has published h papers each of which has been cited by others at least h times. Thus, the h-index reflects both the number of publications and the number of citations per publication

Hs-index

Hs-index is identicial with the H-index if the author has no self-citations. Otherwise the number of source citations are decreased by the number of self-citations in the case of each publication.

A-index

The a-index can be used as a second metric-index for the evaluation and ranking of scientists. It describes the “magnitude” of each scientist’s “hits”. A large a implies that some article(s) have received a fairly large number of citations compared to the rest of its articles and with respect to what the h-index presents. The original definition is as follows Nc = a·h^2

Calculation is as follows: Total number of citations Nc divided by the square of H: a=Nc/H^2

G-index

The index is calculated based on the distribution of citations received by a given researcher's publications.

Given a set of articles ranked in decreasing order of the number of citations that they received, the g-index is the (unique) largest number such that the top g articles received (together) at least g2 citations.

An alternative definition is

Given a set of articles ranked in decreasing order of the number of citations that they received, the g-index is the (unique) largest number such that the top g articles received on average at least g citations.