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)] 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 $\alpha =0$. However, it undergoes a transition from a rough phase ($\alpha >0$) to a smooth phase on scale-free networks as the degree exponent $\gamma$ increases. When $\gamma =4$, we find that the steady-state value of $W(N,t)$ scales as $W_{\mathrm{sat}}\left(N\right)\sim logN$, indicating that the threshold for the transition is ${\gamma }^{*}\simeq 4$.

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• Collective behavior in networks
• Network phase transitions
• Spreading
• Erdos-Renyi graph
• Online social networks
• Scale free & inhomogeneous networks