  We investigate the phenomena of order-disorder phase transition and the
universality of the majority-rule model defined on three complex networks,
namely the Barabasi-Albert, Watts-Strogatz, and Erdos-Renyi networks. Assume
each agent holds two possible opinions distributed randomly across the
networks' nodes. Agents adopt anticonformity and independence behaviors,
represented by the probability (p), where with a probability (p), agents adopt
anticonformity or independence behavior. Based on our numerical simulation
results and finite-size scaling analysis, it is found that the model undergoes
a continuous phase transition for all networks, with critical points for the
independence model greater than those for the anticonformity model in all three
networks. We obtain critical exponents identical to the opinion dynamics model
defined on a complete graph, indicating that the model exhibits the same
universality class as the mean-field Ising model.
