  We investigate the effects of long-range social interactions in flocking
dynamics by studying the dynamics of a scalar model of collective motion
embedded in a complex network representing a pattern of social interactions, as
observed in several social species. In this scalar model we find a
phenomenology analogous to that observed in the classic Vicsek model: In
networks with low heterogeneity, a phase transition separates an ordered from a
disordered phase. At high levels of heterogeneity, instead, the transition is
suppressed and the system is always ordered. This observation is backed up
analytically by the solution of a modified scalar model within an heterogeneous
mean-field approximation. Our work extends the understanding of the effects of
social interactions in flocking dynamics and opens the path to the analytical
study of more complex topologies of social ties.
