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There is a rapid increase of network analysis in several scientific disciplines beginning some decades ago. In the literature 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 a new complex measure of the degree centrality is 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). This new measure is applied to a bibliographic co-authorship network and its reflection on the Web as an example. The new measures of degree centrality show the whole network on the Web has a more centralized structure than the bibliographic network.