Large-scale diffusion MRI tractography remains a significant challenge. Users must orchestrate a complex sequence of instructions that requires many software packages with complex dependencies and high computational costs. We developed MaPPeRTrac, an edge-centric tractography pipeline that simplifies and accelerates this process in a wide range of high-performance computing (HPC) environments. It fully automates either probabilistic or deterministic tractography, starting from a subject's magnetic resonance imaging (MRI) data, including structural and diffusion MRI images, to the edge density image (EDI) of their structural connectomes. Dependencies are containerized with Singularity (now called Apptainer) and decoupled from code to enable rapid prototyping and modification. Data derivatives are organized with the Brain Imaging Data Structure (BIDS) to ensure that they are findable, accessible, interoperable, and reusable following FAIR principles. The pipeline takes full advantage of HPC resources using the Parsl parallel programming framework, resulting in the creation of connectome datasets of unprecedented size. MaPPeRTrac is publicly available and tested on commercial and scientific hardware, so it can accelerate brain connectome research for a broader user community. MaPPeRTrac is available at: https://github.com/LLNL/mappertrac .