We study the effects of the reciprocal links on the dynamics of direct Boolean networks with scale-free topology (SFRBNs). By means of the method of the Derrida Plot, we have investigated the SFRBNs characterized by different values of average degree and different values of reciprocity in order to test the behavioral regimes of the system. The following step was to perform numerical simulation with the quenched Kauffman model to study the dynamical properties of critical SFRBNs with [Formula: see text]. The distribution of the number of different attractors, the period of the cyclic attractors, the transient duration and the fraction of the frozen nodes, have been studied as a function of the reciprocity and network size. The results presented reveal that reciprocity seems to have no direct effect on the changing of the behavioral regime of SFRBNs with given value of [Formula: see text]. On the contrary, we observed that reciprocal links have a profound effect on the dynamic of critical SFRBNs.
Critical Boolean networks with scale-free in-degree distribution