In this paper we consider the question what is the scientific and career performance of principal investigators (PI's) of publicly funded research projects compared to scientific performance of all researchers. Our study is based on high quality data about (i) research projects awarded in Slovenia in the period 1994-2016 (7508 projects with 2725 PI's in total) and (ii) about scientific productivity of all researchers in Slovenia that were active in the period 1970-2016-there are 19 598 such researchers in total, including the PI's. We compare average productivity, collaboration, internationality and interdisciplinarity of PI's and of all active researchers. Our analysis shows that for all four indicators the average performance of PI's is much higher compared to average performance of all active researchers. Additionally, we analyze careers of both groups of researchers. The results show that the PI's have on average longer and more fruitful career compared to all active researchers, with regards to all career indicators. The PI's that have received a postdoc grant have at the beginning outstanding scientific performance, but later deviate towards average. On long run, the PI's leading the research programs (the most prestigious grants) on average demonstrate the best scientific performance. In the last part of the paper we study 23 co-authorship networks, spanned by all active researchers in the periods 1970-1994, . . . , 1970-2016. We find out that they are well connected and that PI's are well distributed across these networks This a final preprint version; the final version of the manuscript can be found at https: //doi.2 Andrej Kastrin et al.forming their backbones. Even more, PI's generate new PI's, since more than 90% of new PI's are connected (have at least one joint scientific publication) with existing PI's. We believe that our study sheds new light to the relations between the public funding of the science and the scientific output and can be considered as an affirmative answer to the question posed in the title.

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The betweenness centrality of a vertex in a graph is the sum of relative numbers of shortest paths that pass through that vertex. We study extremal values of vertex betweenness within various families of graphs. We prove that, in the family of 2-connected (resp. 3-connected) graphs on n vertices, the maximum betweenness value is reached for the maximum degree vertex of the fan graph F 1,n−1 (resp. the wheel graph W n); the maximum betweenness values, their realizing vertices and extremal graphs are determined also for wider families of graphs of minimum degree at least 2 or 3, respectively, and, in addition, for graphs with prescribed maximum degree or prescribed diameter at least 3.