Recently an efficient search technique locating communities or networkmodules (densely connected groups of nodes) was introduced fordirected networks (Palla et al: New Journal of Physics 9, 186 (2007)). Here we investigate the centrality properties of directed module membersin social networks obtained from e-mail exchanges and fromsociometric questionnaires.Our results indicate that nodes in the overlaps betweenmodules play a central role in the studied systems. Furthermore,the two different types of networks show interesting differencesin the relation between the centrality measures and therole of the nodes in the directed modules.