A scheme of evaluating an impact of a given scientific paper based on importance of papers quoting it is investigated. Introducing
a weight of a given citation, dependent on the previous scientific achievements of the author of the citing paper, we define
the weighting factor of a given scientist. Technically the weighting factors are defined by the components of the normalized
leading eigenvector of the matrix describing the citation graph. The weighting factor of a given scientist, reflecting the
scientific output of other researchers quoting his work, allows us to define weighted number of citation of a given paper,
weighted impact factor of a journal and weighted Hirsch index of an individual scientist or of an entire scientific institution.
(Rousseau 1987 ), who claims that publications mentioned in the reference list have an impact on the publication in question, and also, recently, there has been a proposal for applying the philosophy of Page Rank (Brin and Page 1998 ) on a CitationGraph
The main purposes of this article are to uncover interesting features in real-world citationnetworks, and to highlight important substructures. In particular, it applies lattice theory tocitation analysis. On the applied side, it shows that lattice substructures exist in real-word citationnetworks. It is further shown that, through its relations with co-citations and bibliographiccoupling, the diamond (a four-element lattice) is a basic structural element in citation analysis.Finally, citation compactness is calculated for the four- and five element lattices.
recognized the linking properties of citations (Price 1965 ), and Garner applied mathematical notion of graph to citation network (Garner 1967 ). In the citationgraph, each node represents a document and the directed links between each node indicate the
Comparing properties of citing and cited source items opens a wide variety of analytical possibilities. In a study of citations
among papers in the journal Scientometrics a number of analytical themes are identified. The analysis shows: the way in which a citation graph can be decomposed into
different subparts; country specific citation patterns; the effects of self-citations and domestic citations; the mapping
of cited author relationships using direct citation and co-citation links; and time slicing effects on impact ranking of countries
The first-citation distribution, i.e. the cumulative distribution of the time period between publication of an article and the time it receives its first citation, has never been modelled by using well-known informetric distributions. An attempt to this is given in this paper. For the diachronous aging distribution we use a simple decreasing exponential model. For the distribution of the total number of received citations we use a classical Lotka function. The combination of these two tools yield new first-citation distributions.
The model is then tested by applying nonlinear regression techniques. The obtained fits are very good and comparable with older experimental results of Rousseau and of Gupta and Rousseau. However our single model is capable of fitting all first-citation graphs, concave as well as S-shaped; in the older results one needed two different models for it.
Our model is the function
Here γ is the fraction of the papers that eventually get cited, t1 is the time of the first citation, a is the aging rate and α is Lotka's exponent. The combination of a and α in one formula is, to the best of our knowledge, new. The model hence provides estimates for these two important parameters.
We find evidence for the universality of two relative bibliometric indicators of the quality of individual scientific publications taken from different data sets. One of these is a new index that considers both citation and reference counts. We demonstrate this universality for relatively well cited publications from a single institute, grouped by year of publication and by faculty or by department. We show similar behaviour in publications submitted to the arXiv e-print archive, grouped by year of submission and by sub-archive. We also find that for reasonably well cited papers this distribution is well fitted by a lognormal with a variance of around σ2 = 1.3 which is consistent with the results of Radicchi et al. (Proc Natl Acad Sci USA 105:17268–17272, ). Our work demonstrates that comparisons can be made between publications from different disciplines and publication dates, regardless of their citation count and without expensive access to the whole world-wide citation graph. Further, it shows that averages of the logarithm of such relative bibliometric indices deal with the issue of long tails and avoid the need for statistics based on lengthy ranking procedures.
) track evolving communities in the whole CiteSeer paper citationgraph. An et al. ( 2004 ) have constructed article citationgraphs in several research domains by querying CiteSeer and have explored them in terms of components. Popescul et al. ( 2003
prune the data by specifying a period as shown in Fig. 2 . The “data filtering” tab ( Fig. 3 ) allows the user to trim down the number of nodes in the citationgraph by selecting a citation count threshold to filter out less-cited papers. The user may
cognitive analysis, we can see the improvement more clearly as shown in Table 1 . In citationgraph based clustering, the distribution is pretty biased. For example, as demonstrated in Fig. 1 , the smallest cluster (cluster #20 is about the social science