Betweenness centrality (BC) is a crucial graph problem that measures the signi cance of a vertex by the number of shortest paths leading through it. We propose Maximal Frontier Betweenness Centrality (MFBC): a succinct BC algorithm based on novel sparse matrix multiplication routines that performs a factor of p 1/3 less communication on p processors than the best known alternatives, for graphs with n vertices and average degree k = n/p 2/3 . We formulate, implement, and prove the correctness of MFBC for weighted graphs by leveraging monoids instead of semirings, which enables a surprisingly succinct formulation. MFBC scales well for both extremely sparse and relatively dense graphs. It automatically searches a space of distributed data decompositions and sparse matrix multiplication algorithms for the most advantageous con guration. The MFBC implementation outperforms the well-known CombBLAS library by up to 8x and shows more robust performance. Our design methodology is readily extensible to other graph problems.

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