In some networks nodes belong to predefined groups (e.g., authors belong to institutions). Common network cen-trality measures do not take this structure into account. Gefura measures are designed as indicators of a node’s brokerage role between such groups. They are defined as variants of betweenness centrality and consider to what extent a node belongs to shortest paths between nodes from different groups. In this article we make the following new contributions to their study: (1) We systematically study unnormalized gefura measures and show that, next to the ‘structural’ normalization that has hitherto been applied, a ‘basic’ normalization procedure is possible. While the former normalizes at the level of groups, the latter normal-izes at the level of nodes. (2) Treating undirected networks as equivalent to symmetric directed networks, we expand the defini-tion of gefura measures to the directed case. (3) It is shown how Brandes’ algorithm for betweenness centrality can be adjusted to cover these cases.