Due to technological advances in electron microscopy (EM) and deep learning, it is now practical to reconstruct a connectome, a description of neurons and the connections between them, for significant volumes of neural tissue. The limited scope of past reconstructions meant they were primarily used by domain experts, and performance was not a serious problem. But the new reconstructions, of common laboratory creatures such as the fruit fly Drosophila melanogaster, upend these assumptions. These natural neural networks now contain tens of thousands of neurons and tens of millions of connections between them, with yet larger reconstructions pending, and are of interest to a large community of non-specialists. This requires new tools that are easy to use and efficiently handle large data. We introduce neuPrint to address these data analysis challenges. neuPrint is a database and analysis ecosystem that organizes connectome data in a manner conducive to biological discovery. In particular, we propose a data model that allows users to access the connectome at different levels of abstraction primarily through a graph database, neo4j, and its powerfully expressive query language Cypher. neuPrint is compatible with modern connectome reconstruction workflows, providing tools for assessing reconstruction quality, and offering both batch and incremental updates to match modern connectome reconstruction flows. Finally, we introduce a web interface and programmer API that targets a diverse user skill set. We demonstrate the effectiveness and efficiency of neuPrint through example database queries.