Institute of Information Technology of ANAS Rahila Hasanova "New Challenges in the European Area: International Baku Forum of Young Scientists

A scientist has index h if h of his or her N p papers have at least h citations each and the other (N p – h) papers have ≤h citations each. 2 first h papers More than h citations Papers Citations citations= papers= h J.E.Hirsch, An index to quantify an individual’s scientific research output // Proceedings of the National Academy of Sciences of the USA, 2005, vol.102, no.46, pp

 Quantity (publications) and impact (citations).  Awarding prizes  Single-number criteria  Easy to understand 3

Differences among fields. Scientist's career.. Citation to journal articles… Decrease…. Highly cited papers….. Self-citations….. 4 Solomon H. Snyder: h = 191 Hector Garcia-Molina: h = 88

Suppose that, the scientific researcher has 9 papers and these papers received 20, 15, 7, 5, 5, 5, 4, 2, 2 citations accordingly. 5 Articles’ rank of the researcher Number of citations Hirsch core h = 5

The highest rank such that the top g papers have, together, at least g 2 citations. This also means that the top g+1 have less than (g+1) 2 papers. Example. Suppose that, the scientific researcher has 9 papers and these papers received 20, 15, 7, 5, 5, 5, 4, 2, 2 citations accordingly. 6 Let's compare his h-and g-indices. Articles’ rank of a researcher Number of citations L.Egghe, Theory and practice of the g-index // Scientometrics, 2006, vol.69, no.1, pp

7 Citations for each paper The rank of the paper Sum of citations The square rank of the paper h-core g-core h = 5, g = 7

m-index the median number of citations received by papers in the Hirsch core. Example. Suppose that, the scientific researcher has 8 papers and these papers received 23, 20, 19, 12, 7, 4, 3 and 1 citations accordingly. 8 Articles’ rank of the researcher Number of citations h = 5 m = 19 Papers including to Hirsch core Q.L.Bornmann, R.Mutz, and H.D.Daniel, Are there better indices for evaluation purposes than the h-index using data from biomedicine // Journal of the American Society for Information Science and Technology, 2008, vol.59, no.5, pp

Arithmetic mean 9 Root mean square Geometric mean Harmonic mean *Aliguliyev, R., Hasanova, R., The evaluation of the scientific output of researchers / The 3rd International Conference “Problems of Cybernetics and Informatics”, 6-8 Sept. 2010, Baku: **Jipa S., Gorghiu L.M., Dumitrescu C., Oros C. Research output new evaluation of chemistry group in Valahia university with the use of various bibliometric indicators // Journal of Science and Arts, 2012, no. 3, vol. 20, pp

For compare researchers with the same h-index, to the number of citations coming to each paper in Hirsch core, added arithmetic mean of authors’ h-indexes (who cited these researchers’ papers) as weighted coefficient. 10

Assume that, I scientific researcher has 6 papers and these papers received citations accordingly. II scientific researcher has 6 papers and these papers received 6, 3, 2, 0, 0, 0 citations accordingly. 11

For the first researcher h=2 For the second researcher h=2 12 RankI researcherRankII researcher 1<5<51<6 2<4 *2<3 * 3>23 4> >06>1 Let’s sort number of citations coming to the papers of both researchers in decreasing order: *Here the power of citations coming to the papers is not taken account (for ex., h-index of citation’s author, impact factor of the journal from where citation coming and etc.).

For I researcher h=2, g=3, m= Number of citations Rank Sum of citations Square rank Let’s sort number of citations coming to the papers of both researchers in decreasing order : *Here the power of citations coming to the papers is not taken account (for ex., h-index of citation’s author, impact factor of the journal from where citation coming and etc.). For II researcher h=2, g=3, m=4.5 Number of citations Rank Sum of citations Square rank

Here, For the first researcher’s h-index his the first and the second paper gives 1 point each. So, h(I) = 1 (for number of citations coming to the first paper) + 1 (for number of citations coming to the second paper) = 2 For the second researcher’s h-index his the first and the second paper gives 1 point each. So, h(II) = 1 (for number of citations coming to the first paper) + 1 (for number of citations coming to the second paper) = 2 14

15 Number of citation of the first paper for I researcher is 5, number of citations of the second paper is 4. I paper I citation II citation III citation IV citation V citation II paper I citation II citation III citation IV citation *Here number of citations >= 2, that is way they are taken into account. h=2

16 H-index of authors of citations coming to the first paper of I researcher is equal to 4, 3, 2, 0, 0 accordingly. H-index of authors of citations coming to the second paper of I researcher is equal to 7, 6, 1, 1 accordingly. I paper I citation II citation III citation IV citation V citation II paper I citation II citation III citation IV citation h=4 h=3 h=2 h=0 h=7 h=6 h=1 *Here h-index of each citation’s author is taken account. Thus, if any of citations has 2 or more co-authors, then h-index is calculated as arithmetic mean of these authors’ h-index. Self-citation is calculated as h=0.

Normally, the first and the second papers give 1 point each to h-index of the I researcher. Here we include weighted coefficients to these points: 17

18 Number of citation of the first paper for II researcher is 6, number of citations of the second paper is 3. I paper I citation II citation III citation IV citation VI citation II paper II citation III citation V citation I citation *Here number of citations >= 2, that is way they are taken into account. h=2

19 H-index of authors of citations coming to the first paper of II researcher is equal to 6, 6, 1, 1, 0, 0 accordingly. H-index of authors of citations coming to the second paper of II researcher is equal to 1, 1, 0 accordingly. I paper I citation II citation III citation IV citation VI citation II paper II citation III citation V citation I citation h=6 h=1 h=0 h=1 h=0 *Here h-index of the citation’s author is taken account. Thus, if any of citations has 2 or more co-authors, then h-index is calculated as arithmetic mean of these authors’ h-index. Self-citation is calculated as h=0.

Normally, the first and the second papers give 1 point each to h-index of the II researcher. Here we include weighted coefficients to these points: 20 *As seems from example, h(I)>h(II). This means that, the power of citations of the I researcher’s papers is higher than the power of citations of the II researcher’ papers. h(I) = 5.55 h(II) = 3.33

Institute of Information Technology of ANAS “Weighted Hirsch index”, Rahila Hasanova