  Flocking is a fascinating phenomenon observed across a wide range of living
organisms. We investigate, based on a simple self-propelled particle model, how
the emergence of ordered motion in a collectively moving group is influenced by
the local rules of interactions among the individuals, namely, metric versus
topological interactions as debated over in the current literature. In the case
of the metric ruling, the individuals interact with the neighbours within a
certain metric distance; in contrast, in the topological ruling, interaction is
confined within a number of fixed nearest neighbours. Here, we explore how the
range of interaction versus the number of fixed interacting neighbours affects
the dynamics of flocking in an unbounded space, as observed in natural
scenarios. Our study reveals the existence of a certain threshold value of the
interaction radius in the case of metric ruling and a threshold number of
interacting neighbours for the topological ruling to reach an ordered state.
Interestingly, our analysis shows that topological interaction is more
effective in bringing the order in the group, as observed in field studies. We
further compare how the nature of the interactions affects the dynamics for
various sizes and speeds of the flock.
