  Numerical models indicate that collective animal behaviour may emerge from
simple local rules of interaction among the individuals. However, very little
is known about the nature of such interaction, so that models and theories
mostly rely on aprioristic assumptions. By reconstructing the three-dimensional
position of individual birds in airborne flocks of few thousands members, we
prove that the interaction does not depend on the metric distance, as most
current models and theories assume, but rather on the topological distance. In
fact, we discover that each bird interacts on average with a fixed number of
neighbours (six-seven), rather than with all neighbours within a fixed metric
distance. We argue that a topological interaction is indispensable to maintain
flock's cohesion against the large density changes caused by external
perturbations, typically predation. We support this hypothesis by numerical
simulations, showing that a topological interaction grants significantly higher
cohesion of the aggregation compared to a standard metric one.
