We consider a generic probabilistic herding model that has previously been shown to suffer from the problem of N-dependence. The term N-dependence refers to the phenomenon that the unconditional distribution of the herding model approaches a Gaussian distribution (with decreasing variance) under enlargement of system size.

Starting from microscopic foundations, we first derive the analytical form of the unconditional distribution under a mean-field approximation. Second, in order to investigate the impact of network structure on the herding model, we study the behavior of the system under an enlargement of system size for different prototypical network structures.

Lo and behold, small-world and scale-free networks are not capable of overcoming the problem of N-dependence in the probabilistic herding model. As far as N-dependence is concerned, the relative communication range of agents turns out to be the crucial parameter of the herding model. 

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