The set of citations received by a set of publications consists of citations received by articles in the h-core and citations received by articles in the h-tail. Denoting the cardinalities of these fours sets as C, P, CH and CT we introduce the tail-core ratio (CT/CH) and show that in practical cases this ratio tends to increase. Introducing further the k-index, defined as k = (C/P)/(CT/CH), we show that this index decreases in most practical cases. A power law model is in accordance with these practical observations.
be regarded as the elite set (h-core). Consequently, if the h-index is 20, the number of papers in the elite set is equal to 20.
Instead of the above methods for selecting the elite set of papers, Eq. 3 . was recommended (Vinkler 2010b
) can be applied to characterise the degree distribution of the nodes in networks as well.
Analogously to the original h-index, the h-core (cf. Rousseau 2006 ) of a network can be considered a set of core documents obtained by a self
lost if the measure is normalised this way. The changes in the h -index and the h -core along with the age structure of publications and citations allow a deeper insight into an individual's career and might reflect breaks, a caesura or shift in the
“the most important impact indicator of the Leiden Ranking” (Centre for Science and Technology Studies 2011 ). The synchronous 2-year h-index of the journal (h-index). The number of citations within the h-core (h-core cits). The number of
The tail properties of scientometric distributions are studied in the light of the h-index and the characteristic scores and
scales. A statistical test for the h-core is presented and illustrated using the example of four selected authors. Finally,
the mathematical relationship between the h-index and characteristic scores and scales is analysed. The results give new insights
into important properties of rank-frequency and extreme-value statistics derived from scientometric and informetric processes.
For each paper in the h -core (i.e., the papers on ranks r = 1, 2,…, h ) we can apply Schubert's single publication H -index, denoted H r for the paper on rank r . In a forthcoming paper we will study this sequence H 1 , H 2 ,…, H h in
(say in the h- core) we have a single publication h- index, denoted H 1 , …, H h (we distinguish between h , the h- index of the set of papers and H i , the single publication H- index of the i th paper in this h- core ( i = 1, …, h
, H. – Ćorić , T. ( 2014 ): The Effects of Fiscal Policy in a Small Open Transition Economy: The Case of Croatia . Acta Oeconomica , 64 ( S1 ): 133 – 152 .
Eurostat ( 2017 ): National Accounts (ESA 2010
Mathematically, it can be expressed as:
where cit j is the number of citations of the j th paper. The papers that contribute to the calculation of the h -index are usually referred to as the h -core papers.
Undoubtedly, the h -index