We can now measure the connectivity of every neuron in a neural circuit, but we are still blind to other biological details, including the dynamical characteristics of each neuron. The degree to which connectivity measurements alone can inform understanding of neural computation is an open question. We show that with only measurements of the connectivity of a biological neural network, we can predict the neural activity underlying neural computation. Our mechanistic model makes detailed experimentally testable predictions for each neuron in the connectome. We found that model predictions agreed with experimental measurements of neural activity across 24 studies. Our work demonstrates a strategy for generating detailed hypotheses about the mechanisms of neural circuit function from connectivity measurements.