It has now become possible to map the synaptic connectivity of neural circuitry at the cellular resolution using electron microscopy . In this work, we present a new class of models for the analysis of connectomic data. Many theories of neural computation propose specic patterns of neural connectivity tied to the tuning properties of neurons. We propose an extension to traditional latent space models  to uncover continuous hidden structure in these connectomes, such as the neural tuning property of a neuron and the function that determines neural connectivity. Our scalable model provides the exibility to recover structure in both directed and undirected graphs. We demonstrate our model on synthetic connectomes and on the recently published mouse retinal connectome.