  The design of distributed autonomous systems often omits consideration of the
underlying network dynamics. Recent works in multi-agent systems and swarm
robotics alike have highlighted the impact that the interactions between agents
have on the collective behaviours exhibited by the system. In this paper, we
seek to highlight the role that the underlying interaction network plays in
determining the performance of the collective behaviour of a system, comparing
its impact with that of the physical network. We contextualise this by defining
a collective learning problem in which agents must reach a consensus about
their environment in the presence of noisy information. We show that the
physical connectivity of the agents plays a less important role than when an
interaction network of limited connectivity is imposed on the system to
constrain agent communication. Constraining agent interactions in this way
drastically improves the performance of the system in a collective learning
context. Additionally, we provide further evidence for the idea that `less is
more' when it comes to propagating information in distributed autonomous
systems for the purpose of collective learning.
