  Volumetric brain reconstructions provide an unprecedented opportunity to gain
insights into the complex connectivity patterns of neurons in an increasing
number of organisms. Here, we model and quantify the complexity of the
resulting neural connectomes in the fruit fly, mouse, and human and unveil a
simple set of shared organizing principles across these organisms. To put the
connectomes in a physical context, we also construct contactomes, the network
of neurons in physical contact in each organism. With these, we establish that
physical constraints -- either given by pairwise distances or the contactome --
play a crucial role in shaping the network structure. For example, neuron
positions are highly optimal in terms of distance from their neighbors.
However, spatial constraints alone cannot capture the network topology,
including the broad degree distribution. Conversely, the degree sequence alone
is insufficient to recover the spatial structure. We resolve this apparent
conflict by formulating scalable maximum entropy models, incorporating both
types of constraints. The resulting generative models have predictive power
beyond the input data, as they capture several additional biological and
network characteristics, like synaptic weights and graphlet statistics.
