Majority rule on heterogeneous networks

We focus on the majority rule (MR) applied on heterogeneous networks. When the underlying topology is homogeneous, the system is shown to exhibit a transition from an ordered regime to a disordered regime when the noise is increased. When the network exhibits modular structures, in contrast, the system may also exhibit an asymmetric regime, where the nodes in each community reach an opposite average opinion. Finally, the node degree heterogeneity is shown to play an important role by displacing the location of the order-disorder transition and by making the system exhibit non-equipartition of the average spin.