index_h {agop}R Documentation

Hirsch's h-index


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

H(x)=\max\{i=1,\dots,n: x_i \ge i\}

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



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



a non-negative numeric vector


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

For historical reasons, this function is also available via an 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 (see 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.

Mesiar R., Gagolewski M., H-index and other Sugeno integrals: Some defects and their compensation, IEEE Transactions on Fuzzy Systems 24(6), 2016, pp. 1668-1672. doi:10.1109/TFUZZ.2016.2516579

Gagolewski M., Mesiar R., Monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem, Information Sciences 263, 2014, pp. 166-174. doi:10.1016/j.ins.2013.12.004

Gagolewski M., Data Fusion: Theory, Methods, and Applications, Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp. isbn:978-83-63159-20-7

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_lp(), index_maxprod(), index_rp(), 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 0.2.4 Index]