
Egghe, L.
We present a study of four impact measures: the hindex, the gindex, the Rindex and the jindex. The gindex satisfies the transfer principle, the jindex satisfies the opposite transfer principle while the h and Rindices do not satisfy any of these principles. We study general inequalities between these measures and also determine their maximal and minimal values, given a fixed total number of citations.

Goovaerts, Marc; Leinders, Dirk
In this paper, we evaluate the quality of the metadata of an OAIcompliant repository based on the completeness metric proposed by X. Ochoa and E. Duval. This study focuses on the completeness of the metadata records as defined by M.A. Sicilia et al, where machineunderstandability is a mandatory requirement for completeness. The goal is to use the completeness metric as a tool for harvesters and repository managers to evaluate easily the quality of the metadata of a repository. We focus on the metadata used by the communities of agriculture, aquaculture and environment from the VOA3R project. The OceanDocs repository serves...

Egghe, L.
In this paper and talk we present a short proof of a theorem of Naranan stating that if sources grow exponentially and if items in sources also grow exponentially, then the system is Lotkaian, i.e. its sizefrequency function is the law of Lotka.
We apply this technique to the case of power law growth of sources and of items in sources and determine the size and rank frequency functions in this case. These functions have a greater variety of shapes than in the classical Naranan case and we give practical examples. We also show that, in this context, the law...

Egghe, L.
We describe mathematically the ageindependent version of the hindex, defined by Abt (Scientometrics 91(3), 863868, 2012) and explain when this indicator is constant with age.
We compare this index with the one where not the hindex is divided by career length but where all citation numbers are divided by career length and where we then calculate the new hindex. Both mathematical models are compared.
A variant of this second method is by calculating the hindex of the citation data, divided by article age. Examples are given.

Egghe, L.
Informetrics

Egghe, L.
In [A. Pulgarin. Dependence of Lotka’s law parameters on the scientific area. Malaysian Journal of Library and Information Science 17(1), 4150, 2012] the author finds negative correlations between the average number of papers per author and the Lotka exponent and the Lotka constant as well as positive correlations between the latter two parameters. He also finds lower values for the latter two parameters in fields or countries with highly concentrated productions (e.g. where there is heavy growth). In the present paper these findings are proved mathematically, based on earlier results on Lotka's law proved by this author.

Egghe, L.
We give a heuristic proof of the relation between the impact factor (IF) and the uncitedness factor (U), the fraction of the papers that are uncited: U = 1/1+IF . This generalizes the proof of Hsu and Huang [Physica A 391, 21292134, 2012] who obtain the same result but based on the assumption of the validity of the Mattheweffect. This new informetric function opens the discusion on universal informetric laws, distribution dependent laws and parameter dependent laws of which examples from the informetrics literature are given.

Egghe, L.; Guns, R.; Rousseau, R.
The visibility of an article depends to a large extent on its authors. We study the question how each coauthor's relative contribution to the visibility of the article can be determined and quantified using an indicator, referring to such an indicator as a CAVindicator. A twostep procedure is elaborated, whereby one first chooses an indicator (e.g. total number of citations, hindex,...) and subsequently one of two possible approaches. The case where the indicator is an htype index is elaborated in a Lotkaian framework. Different examples illustrate the procedure and the choices involved in determining a CAVindicator.

Egghe, L.
The central area indices and the central interval indices, as introduced in DortaGonzález, Scientometrics 88(3), 729745, 2011, are studied from a theoretical point of view. They are defined in order to yield higher impact values of "selective" authors (i.e. authors with concentrated number of citations over their publications). We show that this property is not valid for every citation distribution. However,if Zipf's law is adopted for the citation distribution, we can show that the central area indices and the central interval indices have indeed higher values for more selective authors.

Egghe, L.
We present a model that describes which fraction of the literature on a certain topic we will find when we use n(n=1,2,...)databases. It is a generalization of the theory of discovering usability problems. We prove that, in all practical cases, this fraction is a concave function of n, the number of used databases, hereby explaining some graphs that exist in the literature. We also study limiting features of this fraction for n very high and we characterize the case that we find all literature on a certain topic for n high enough.

Egghe, L.; Bornmann, L.
Purpose: We further exploit the analogy between journal peer review and information retrieval. In this way we want to quantify some imperfections of journal peer review. Design/methodology/approach: We define fallout rate and missing rate in order to describe quantitavely the weak papers that were accepted and the strong papers that we missed, respectively. To assess the quality of manuscripts we use bibliometric measures. Findings: Fallout rate and missing rate are put in relation with the hitting rate and success rate. Conclusions are drawn on what friction of weak papers will be accepted in order to have a certain fraction of...

Egghe, L.
In [A.Pulgarin. Dependence of Lotka's law parameters on the scientific area. Malaysian Journal of Library and Information Science 17(1), 4150, 2012] the author finds negative correlations between the average number of papers per author and the Lotka exponent and the Lotka constant as well as positive correlations between the latter two parameters. He also finds lower values for the latter two parameters in fields or countries with highly concentrated productions(e.g. where there is heavy growth). In the present paper these findings are proved mathematically, based on earlier results on Lotka's law proved by this author.

Egghe, L.
The citer hindex of a researcher (introduced by Ajiferuke and Wolfram) was found to have a strong linear relationship with the hindex of this researcher. This finding of Franceschini, Maisano, Perotti and Proto also revealed, experimentally, that the slope of this straight line (passing through the origin) is strictly larger than one. In this paper we present a rationale for this empirical result of this author on the relation between the hindex before and after a transformation of the citation data.

Egghe, L.; Guns, R.
In a previous work (Egghe, 2011), the first author showed that Benford's law (describing the logarithmic distribution of the numbers 1, 2,..., 9 as first digits of data in decimal form) is related to the classical law of Zipf with exponent 1. The work of Campanario and Coslado (2011), however, shows that Benford's law does not always fit practical data in a statistical sense. In this article, we use a generalization of Benford's law related to the general law of Zipf with exponent ?????>???0. Using data from Campanario and Coslado, we apply nonlinear least squares to determine the optimal ??...

Egghe, Leo; Guns, Raf; Rousseau, Ronald
Contrary to what one might expect, Nobel laureates and Fields medalists have a rather large fraction (10% or more) of uncited publications. This is the case for (in total) 75 examined researchers from the fields of mathematics (Fields medalists), physics, chemistry, and physiology or medicine (Nobel laureates). We study several indicators for these researchers, including the hindex, total number of publications, average number of citations per publication, the number (and fraction) of uncited publications, and their interrelations. The most remarkable result is a positive correlation between the hindex and the number of uncited articles. We also present a Lotkaian model,...

Egghe, Leo
End of 2011, the Journal of Informetrics (Elsevier) existed five years. We overview its scope, published articles (topics, coauthorship, authors’ countries), editorial decisions, editorial and production times, impact factor and article downloads aspects. Finally we present a local citation environment map of JOI.

Egghe, Leo
Supposing that the number of sources and the number of items in sources grow in time according to power laws, we present explicit formulae for the size and rankfrequency functions in such systems. Sizefrequency functions can decrease or increase while rankfrequency functions only decrease. The latter can be convex, concave, Sshaped (first convex, then concave) or reverse Sshaped (first concave, then convex). We also prove that, in such systems, Heaps’ law on the relation between the number of sources and items is valid.

Egghe, Leo
The single publication Hindex, introduced by A. Schubert in 2009 can be
applied on all articles in the Hirschcore of a researcher. In this way one can deﬁne the
‘‘indirect Hindex’’ of a researcher.

Egghe, Leo
This paper presents a different view on properties of impact measures than given in the paper of De Visscher. We argue that a good impact measure should prefer concentrated (unequal) situations of citations per paper rather than situations where citations are more equally spread out over papers.
We also present theoretical evidence that the gindex and the Rindex can be close to the square root of the total number of citations, while this is not the case for the Aindex. Here we confirm an assertion of De Visscher.

EGGHE, Leo
We show that the rank frequency functions of two researchers usually intersect. As a consequence of this, different htype indices can conclude on different impact judgements of the two researchers. Also in this paper a new indicator is proposed: the average number of citations per paper in the papers whose ranks are smaller than or equal to the intersection point of their two rank frequency functions. The theoretical derivations are illustrated using an empirical example.