877 A Diffusion-based h-type Indicator Dilruba Mahbuba *,** and Ronald Rousseau **,***,**** mahbubadilruba@gmail.com; ronald.rousseau@khbo.be * Library and Information Department, Northern University Bangladesh (NUB) Sher Tower, Holding #13, Road #17, Banani, Dhaka – 1213 ** IOIW, University of Antwerp, Venusstraat 35, B-2000 Antwerpen (Belgium) *** KHBO (Association KU Leuven), Faculty of Engineering Technology, Zeedijk 101, B-8400 Oostende (Belgium) **** KU Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Heverlee (Belgium) Introduction Although the original has the benefit of experience and familiarity, theories, tools and techniques are always modifiable, can be adapted to new circumstances and polished to satisfy the user. In the days of card catalogs, library systems often forced users to travel to a central catalog or one of multiple branches just to discover holdings. Today users can consult all holdings from workstations throughout the system (Besser, 1998). This example illustrates that the idea of ‘access to information’ is not new but it has been adapted to grow in new directions. Similarly, research evaluation and scientometric studies have developed various tools, indicators and measurement indices over many decades. In the latest decade we have seen the rise in the use of the h-index (Hirsch, 2005) as a basic indicator to measure academic performance. Various related indices have been proposed based on Hirsch’ original idea such as the g-index and the R-index (Egghe, 2006; Jin & al., 2007). Although less used, also the diffusion factor (Rowlands, 2002) may be considered as a basic scientometric indicator. Rowlands understood it metaphorically as a measure of the extent of the resulting ripples (citations) as new publications enter the literature (the pond).In this contribution we propose a fusion of these two basic indicators. Data and methods As stated in Liu (2011) diffusion always refers to the spread of something to other things through some medium. In this article we study the spread of scientific ideas (included in articles) by citations in other articles. The notion of diffusion is operationalized by counting citations. The most elementary case is through articles, i.e. we count the number of different articles that cite a source. Diffusion speed is defined as the number of different citing items divided by the age of the studied source article or source articles (all published in the same year). When citing articles are counted this so-called diffusion speed is nothing but the average number of citations per year (for a single article or for a group of articles published in the same year and considered as a whole). Such a table of diffusion speeds leads to an h-index, which, as far as we know, has not been studied before. Calculating an h-index in this way is one way of taking the age of the source into account. However, when the length of the citation window is fixed (the same for each source) then the ranking according to total number of received citations and the ranking according to diffusion speed is the same as each number of citations is divided by the same value, namely the fixed length of the citation window. The corresponding h-indices, however, differ. When the length of the citation window changes, e.g. by always considering the number of received citations up to the year of investigation, then each diffusion speed value may change over the years and usually does. In this way the h-index gains a dynamic aspect. Table 1 gives a short fictitious case where we consider (as an example) an author’s articles and their journal diffusion speed (= number of different citing journals over a 4-year citation window, divided by 4). The corresponding diffusion h-index is 3 (whole counts) or 3.5 when the real-valued h-index (Rousseau, 2006) is used. The real-valued h-index We recall the calculation of the real-valued h-index h r as introduced by Rousseau (2006) and further studied in (Guns & Rousseau, 2009). Definition of h r : Let V(k) denote the value in the column for which we want to determine a real-valued h-index corresponding to the source at rank k, and let V(x) denote the piecewise linear interpolation of V(k)-values. Then h r is the abscissa of the intersection of the function V(x) and the straight line y = x. As h ≤ h r and V(h+1) <h + 1, this intersection is situated on the line segment connecting (h,V(h)) and (h + 1, V(h+1)). Consequently: h ≤ h r < h + 1 and ( 1). ( )- . ( 1) 1- ( 1) () r h Vh hV h h Vh Vh + + = + + .