- We propose and evaluate two complementary heuristics to speed up exact computation of the shortest-path between ness centrality. Both heuristics are relatively simple adaptations of the standard algorithm for between ness centrality. Consequently, they generalize the computation of edge between ness and most other variants, and can be used to further speed up between ness 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 between ness algorithm on the block-cut point tree and then compute the remaining contributions separately in each biconnected component. Experiments on a variety of large graphs illustrate the efficiency and complementarity of our heuristics.