Betweenness centrality was proposed about 35 years ago by Freeman. Since then, it was widely used mainly for analyzing social networks. According to Web of Knowledge, the two original papers on that topic were cited thousands of times, which indicates the interest of the research community. An adjusted version of betweenness centrality, (adjusted centrality), was recently proposed which is slightly different from betweenness centrality, but has more mathematical properties. Despite its research interest, very few papers were published on mathematical properties of betweenness centrality or adjusted centrality. In the current paper, we study the mathematical properties of adjusted centrality among trees.