In the literature there are a large number of publications in sociology, in computer science or in information sciences, as well as in studies of collaboration in science describing the studies of social networks with unweighted ties because measures involving unweighted ties are easier to calculate. It is not surprising that there are few studies on networks with weighted ties since they not only need more complex formulas but need a process of quantification when quantitative empirical data are not directly available. However quantitative empirical data are directly available under the condition of using bibliometric or webometric data.In conclusion new complex measures of the degree centrality are introduced including weighted ties possible for use of the analysis of co-authorship or citation networks. Both co-authorship relations and citations are well quantified data (weighted ties).These new measures are applied to a co-authorship network as an example
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