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Hypergraphs are a popular paradigm to represent complex real-world networksexhibiting multi-way relationships of varying sizes. Mining centrality inhypergraphs via symmetric adjacency tensors has only recently becomecomputationally feasible for large and complex datasets. To enable scalablecomputation of these and related hypergraph analytics, here we focus on theSparse Symmetric Tensor Times Same Vector (S$^3$TTVc) operation. We introducethe Compound Compressed Sparse Symmetric (CCSS) format, an extension of thecompact CSS format for hypergraphs of varying hyperedge sizes and present ashared-memory parallel algorithm to compute S$^3$TTVc. We experimentally showS$^3$TTVc computation using the CCSS format achieves better performance thanthe naive baseline, and is subsequently more performant for hypergraph$H$-eigenvector centrality.

Fast Parallel Tensor Times Same Vector for Hypergraphs