In the study of complex networks, simple local heterogeneous interactions favor highly complicated and non-linear dynamics. In this paper, we take advantage of recent advances presented by Rosas et al [Physical Review E, 100, 032305] to capture the fundamentals of dynamics: high-order interdependencies. In particular, the phase diagram of Random Boolean Networks is described in terms of the information shared between multiple nodes. We found that the critical point between ordered and chaotic regimes is well defined by a balance between redundancy and synergy, for both normal and scale-free topologies. In addition, particular network structures are identified that characterize the behavior of high-order interdependencies in each dynamic regime.