Even in its minimal representation (Vicsek Model, VM [T. Vicsek, A. Czirok, E. Ben‐Jacob, I. Cohen and O. Shochet. Phys. Rev. Lett. 75, 1226 (1995).]), the widespread phenomenon of flocking raises intriguing questions to the statistical physicists. While the VM is very close to the better understood XY Model because they share many symmetry properties, a major difference arises by the fact that the former can sustain long‐range order in two dimensions, while the latter can not. Aiming to contribute to the understanding of this feature, by means of extensive numerical simulations of the VM, we study the network structure of clusters showing that they can also sustain purely orientational, mean‐field‐like, long‐range order. We identify the reason of this capability with the key concept of “effective dimension.” In fact, by analyzing the behavior of the average path length and the mean degree, we show that this dimension is very close to four, which coincides with the upper critical dimension of the XY Model, where orientational order is also of a mean‐field nature. We expect that this methodology could be generalized to other types of dynamical systems.