Roughening of information landscape with asymmetric social contagion process on complex networks

To understand how interaction topology and competition affect the diversity of information in the real world, we study the social contagion model introduced by Halvorsen-Pedersen-Sneppen (HPS) [Phys. Rev. E 103, 022303 (2021)2470-004510.1103/PhysRevE.103.022303] on static complex networks. The diversity of the information is measured through the root mean square of the information value W(N,t), which corresponds to the interface width in roughening phenomena. From the numerical simulations, we find that the HPS model on Erdős-Rényi random networks is always in the smooth phase characterized by the roughness exponent α=0. However, it undergoes a transition from a rough phase (α>0) to a smooth phase on scale-free networks as the degree exponent γ increases. When γ=4, we find that the steady-state value of W(N,t) scales as W_{sat}(N)∼logN, indicating that the threshold for the transition is γ^{*}≃4.