  We study the effects of animal social networks with a weighted pattern of
interactions on the flocking transition exhibited by models of self-organized
collective motion. Considering a model representing dynamics on a
one-dimensional substrate, application of a heterogeneous mean-field theory
provides a phase diagram as function of the heterogeneity of the network
connections and the correlations between weights and degree. In this diagram we
observe two phases, one corresponding to the presence of a transition and other
to a transition suppressed in an always ordered system, already observed in the
non-weighted case. Interestingly, a third phase, with no transition in an
always disordered state, is also obtained. These predictions, numerically
recovered in computer simulations, are also fulfilled for the more realistic
Vicsek model, with movement in a two-dimensional space. Additionally, we
observe at finite network sizes the presence of a maximum threshold for
particular weight configurations, indicating that it is possible to tune
weights to achieve a maximum resilience to noise effects. Simulations in real
weighted animal social networks show that, in general, the presence of weights
diminishes the value of the flocking threshold, thus increasing the fragility
of the flocking state. The shift in the threshold is observed to depend on the
heterogeneity of the weight pattern.
