Social relationships characterize the interactions that occur within social species and may have an important impact on collective animal motion. Here, we consider a variation of the standard Vicsek model for collective motion in which interactions are mediated by an empirically motivated scale-free topology that represents a heterogeneous pattern of social contacts. We observe that the degree of order of the model is strongly affected by network heterogeneity: more heterogeneous networks show a more resilient ordered state, while less heterogeneity leads to a more fragile ordered state that can be destroyed by sufficient external noise. Our results challenge the previously accepted equivalence between the static Vicsek model and the equilibrium $XY$ model on the network of connections, and point towards a possible equivalence with models exhibiting a different symmetry.

• Received 19 September 2017
• Revised 30 November 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.068303