Measuring the functional complexity of nanoscale connectomes: polarity matters

The emerging electron microscopy connectome datasets provides connectivity maps of the brains at single cell resolution, enabling us to estimate various network statistics, such as connectedness. We desire the ability to assess how the functional complexity of these networks depends on these network statistics. To this end, we developed an analysis pipeline and a statistic, XORness, which quantifies the functional complexity of these networks with varying network statistics. We illustrate that actual connectomes have high XORness, as do generated connectomes with the same network statistics, suggesting a normative role for functional complexity in guiding the evolution of connectomes, and providing clues to guide the development of artificial neural networks.