# Which Index?

Algebra Level 3

It is often difficult to compare the 'worth' of the research work done by two researchers. One way to quantify this is to use the number of citations. Currently, there are two indices which are used for this purpose.

h-index : A scientist has index $$h$$ if $$h$$ of his/her $$N_p$$ papers have at least $$h$$ citations each, and the other $$(N_p − h)$$ papers have no more than $$h$$ citations each.

g-index : 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 $$g^2$$ citations.

An author with $$N_p$$ publications has a h-index of $$n_h$$ and a g-index of $$n_g$$. Which of these statements is always true?

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