We are now in the era of millimeter-scale electron microscopy (EM) volumes collected at nanometer resolution. Dense reconstruction of cellular compartments in these EM volumes has been enabled by recent advances in Machine Learning (ML). Automated segmentation methods produce exceptionally accurate reconstructions of cells, but post-hoc proofreading is still required to generate large connectomes free of merge and split errors. The elaborate 3-D meshes of neurons in these volumes contain detailed morphological information at multiple scales, from the diameter, shape, and branching patterns of axons and dendrites, down to the fine-scale structure of dendritic spines. However, extracting these features can require substantial effort to piece together existing tools into custom workflows. Building on existing open-source software for mesh manipulation, here we present "NEURD", a software package that decomposes meshed neurons into compact and extensively-annotated graph representations. With these feature-rich graphs, we automate a variety of tasks such as state of the art automated proofreading of merge errors, cell classification, spine detection, axon-dendritic proximities, and other annotations. These features enable many downstream analyses of neural morphology and connectivity, making these massive and complex datasets more accessible to neuroscience researchers focused on a variety of scientific questions.