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H index
The h-index is an author-level metric that attempts to measure both the productivity
and citation impact of the publication of a Scientist or a Scholar.
Formally,iffisthefunctionthatcorrespondstothenumberofcitationsforeach
publication,wecomputetheh-indexasfollows.Firstweorderthevaluesofffrom
thelargesttothelowestvalue.Then,welookforthelastpositioninwhichfisgreater
thanorequaltotheposition(wecallhthisposition).
Forexample,ifwehavearesearcherwith5publicationsA,B,C,D,andEwith10,8,
5,4,and3citations,respectively,thehindexisequalto4becausethe4th
publicationhas4citationsandthe5thhasonly3.
Incontrast,ifthesamepublicationshave25,8,5,3,and3,thentheindexis3
becausethefourthpaperhasonly3citations.
f(A)=10,f(B)=8,f(C)=5,f(D)=4,f(E)=3→h-index=4
f(A)=25,f(B)=8,f(C)=5,f(D)=3,f(E)=3→h-index=3
If we have the functionfordered in decreasing order from the largest value to the
lowest one,
we can compute thehindex as follows:
h-index (f) =max min(f(i),i)