  The emergence of collective motion, also known as flocking or swarming, in
groups of moving individuals who orient themselves using only information from
their neighbors is a very general phenomenon that is manifested at multiple
spatial and temporal scales. Swarms that occur in natural environments
typically have to contend with spatial disorder such as obstacles that hinder
an individual's motion or communication with neighbors. We study swarming
particles, with both aligning and repulsive interactions, on percolated
networks where topological disorder is modeled by the random removal of lattice
bonds. We find that an infinitesimal amount of disorder can completely suppress
swarming for particles that utilize only alignment interactions suggesting that
alignment alone is insufficient. The addition of repulsive forces between
particles produces a critical phase transition from a collectively moving swarm
to a disordered gas-like state. This novel phase transition is entirely driven
by the amount of topological disorder in the particles environment and displays
critical features that are similar to those of 2D percolation, while occurring
at a value of disorder that is far from the percolation critical point.
