Author-level metrics are citation metrics that measure the bibliometric impact of individual authors, researchers, academics, and scholars. Many metrics have been developed that take into account varying numbers of factors (from only considering the total number of citations, to looking at their distribution across papers or journals using statistical or graph-theoretic principles).
These quantitative comparisons between researchers are mostly done to distribute resources (such money and academic positions). However, there is still debate in the academic world about how effectively author-level metrics accomplish this objective.
Author-level metrics differ from journal-level metrics which attempt to measure the bibliometric impact of academic journals rather than individuals. However, metrics originally developed for academic journals can be reported at researcher level, such as the author-level eigenfactor and the author impact factor.
h-index
Formally, if f is the function that corresponds to the number of citations for each publication, the h-index is computed as follows. First, we order the values of f from the largest to the lowest value. Then, we look for the last position in which f is greater than or equal to the position (we call h this position). For example, if we have a researcher with 5 publications A, B, C, D, and E with 10, 8, 5, 4, and 3 citations, respectively, the h-index is equal to 4 because the 4th publication has 4 citations and the 5th has only 3. In contrast, if the same publications have 25, 8, 5, 3, and 3 citations, then the index is 3 because the fourth paper has only 3 citations.
Author-level Eigenfactor is a version of Eigenfactor for single authors. Eigenfactor regards authors as nodes in a network of citations. The score of an author according to this metric is his or her eigenvector centrality in the network.
It has been argued that "For an individual researcher, a measure such as Erdős number captures the structural properties of the network whereas the h-index captures the citation impact of the publications.