agop - Online Manual

index_h {agop}R Documentation

Hirsch's h-index


Given a sequence of n non-negative numbers x=(x_1,…,x_n), where x_i ≥ x_j ≥ 0 for i ≤ j, the h-index (Hirsch, 2005) for x is defined as

H(x)=max{i=1,…,n: x_i ≥ i}

if n ≥ 1 and x_1 ≥ 1, or H(x)=0 otherwise.



index.h(x) # same as index_h(x), deprecated alias



a non-negative numeric vector


If non-increasingly sorted vector is given, the function is O(n).

For historical reasons, this function is also available via its alias, index.h [but its usage is deprecated].

See index_rp and owmax for natural generalizations.

The h-index is the same as the discrete Sugeno integral of x w.r.t. the counting measure (cf. Torra, Narukawa, 2008).


a single numeric value


Hirsch J.E., An index to quantify individual's scientific research output, Proceedings of the National Academy of Sciences 102(46), 2005, pp. 16569-16572.

Sugeno M., Theory of fuzzy integrals and its applications, PhD thesis, Tokyo Institute of Technology, 1974.

Torra V., Narukawa Y., The h-index and the number of citations: Two fuzzy integrals, IEEE Transactions on Fuzzy Systems 16(3), 2008, pp. 795-797.

See Also

Other impact_functions: index.g, index_g, index_g_zi; index.lp, index_lp; index.rp, index_rp; index_maxprod; index_w; pord_weakdom


authors <- list(  # a list of numeric sequences
                  # (e.g. citation counts of the articles
                  # written by some authors)
    "A" =c(23,21,4,2,1,0,0),
    "B" =c(11,5,4,4,3,2,2,2,2,2,1,1,1,0,0,0,0),
    "C" =c(53,43,32,23,14,13,12,8,4,3,2,1,0)
sapply(authors, index_h)

[Package agop version 0.2-0 Index]