h-index as a metric

h-index is a metric that is used to measure the research impact of researchers all over the world. I have once read a quote that thinks of metrics as if they are proxies to unmeasurable quantities. In other words, one can’t easily say that the research impact/contribution of someone is higher than another one. Thus, these metrics can’t be used on their own to compare and evaluate the previous publications of a researcher.
As for any index metric, the higher the value the better. Consequently, having an h-index of 2 is better than having an h-index of 1.

Definition

According to Google Scholar metrics1:

The h-index of a publication is the largest number h such that at least h articles in that publication were cited at least h times each. For example, a publication with five articles cited by, respectively, 17, 9, 6, 3, and 2, has the h-index of 3.

Reading this for the first time daunted me somehow.

A simple method to compute the h-index

For the example given in the Google scholar description of h-index, How can one easily compute the h-index for “a publication with five articles cited by, respectively, 17, 9, 6, 3, and 2”?

For this publication to have an h-index of 1, they must have at least one article that has at least one citation. Since this criteria is satisified then the publication can have an h-index of 1.
But, can they have an h-index of 2? The answer is yes since they have at least TWO articles (actually they have 5 publications) each with at least 2 citations.
What about having an h-index of 3? The publication has at least THREE articles (actually they had four) with at least three citations.
Finally, you can easily notice that the publication has only three articles with four or more citations thus they don’t qualify to have an h-index of 4.
Therefore, the publication’s h-index will be just 3.

[1] https://scholar.google.com/intl/en/scholar/metrics.html#metrics