We introduce the h-degree of a node as a basic indicator for weighted networks. The h-degree (dh) of a node is the number dh if this node has at least dh links with other nodes and the strength of each of these links is greater than or equal to dh. Based on the notion of h-degree other notions...

The definitions of the rational and real-valued variants of the h-index and g-index are reviewed. It is shown how they can be obtained both graphically and by calculation. Formulae are derived expressing the exact relations between the h-variants and between the g-variants. Subsequently these...

Recently Woeginger [Woeginger, G. H. (2008-a). An axiomatic characterization for the Hirsch-index. Mathematical Social Sciences. An axiomatic analysis of Egghe's g-index. Journal of Informetrics] introduced a set of axioms for scientific impact measures. These lead to a characterization of the...

Three variations on the power law model proposed by Egghe are fitted to four groups of h-index time series: publication-citation data for authors, journals and universities; and patent citation data for firms. It is shown that none of the power law models yields an adequate description of total...

We point out some theoretical problems in the construction of the activity index and related indicators. Concretely, if the activity index is larger than one then it is, at least theoretically, possible to decrease its value by increasing the activity in that field. Although for some practical...

The introduction, construction and upgrading of a system of key labs and open labs are all results of a major S&T system reform in mainland China. A series of programmes extending over a period of 20 years has resulted in more than 160 key labs and nearly 400 open labs at present. Key labs as...

In this contribution we show how results obtained in a series of papers by Egghe can be refined in the sense that we need fewer additional conditions. In these articles Egghe considered a general h-type index which has a value n if n is the largest natural number such that the first n...

The difference among journal reference characteristics in various fields causes a field-based difference in their citation counts. For the purpose of improving indicators used in cross-field evaluations it is necessary to continue explorations corresponding to the characteristics of journal...

Hypes occur in every domain of human behavior, including scientific research. We show in this contribution that journals and authors who studied the h-index benefited in terms of short-term citations. As, moreover, the introduction of the h-index is more a ‘clever find’ than a first rate...

A correction is provided for the proof of a theorem announced in (Rousseau et al., 2013). We show, moreover, that in a network subdivided into three or more subgroups there is at most one node with global Q-measure equal to one. In case there are two subgroups then it is possible to have two...