- We propose and evaluate two complementary heuristics to speed up exact computation of the shortest-path betweenness centrality (BC). Both heuristics are relatively simple adaptations of the standard algorithm for BC. Consequently, they generalize the computation of edge betweenness and most other variants, and can be used to further speed up betweenness estimation algorithms, as well. In the first heuristic, structurally equivalent vertices are contracted based on the observation that they have the same centrality and also contribute equally to the centrality of others. In the second heuristic, we first apply a linear-time betweenness algorithm on the block-cut-point tree and then compute the remaining contributions separately in each bi-connected component. Experiments on a variety of large graphs illustrate the efficiency and complementarity of our heuristics.