  Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model
for network observability transitions in which a sensor placed on a node makes
the node and the adjacent nodes observable. The size of the connected
components comprising the observable nodes is a major concern of the model. We
analyze this model in random heterogeneous networks with degree correlation.
With numerical simulations and analytical arguments based on generating
functions, we find that negative degree correlation makes networks more
observable. This result holds true both when the sensors are placed on nodes
one by one in a random order and when hubs preferentially receive the sensors.
Finally, we numerically optimize networks with a fixed degree sequence with
respect to the size of the largest observable component. Optimized networks
have negative degree correlation induced by the resulting hub-repulsive
structure; the largest hubs are rarely connected to each other, in contrast to
the rich-club phenomenon of networks.
