Magalhães, BrunoSchürmann, Felix2023-05-082023-05-082023-05-08202010.48550/arxiv.2012.06012https://infoscience.epfl.ch/handle/20.500.14299/1975292012.06012Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating distinct subsets of rows to compute nodes. Efficient matrix transpose is an operation of high importance, providing the reverse graph pathways and a column-ordered matrix view. This operation is well studied for simple graph models. Nevertheless, its resolution for multigraphs and higher-cardinality connectivity matrices is unexistent. We advance state-of-the-art distributed transposition methods by providing a theoretical model, algorithmic details, MPI-based implementation and proof of mathematical soundness for such complex models. Benchmark results demonstrate ideal and almost ideal scaling properties for perfectly- and heterogeneously-balanced datasets, respectivelytext::preprint