This paper provides a model to investigate information spreading over cyber-social network of agents communicating with each other. The cyber-social network considered here comprises individuals and news agencies. Each individual holds a belief represented by a scalar. Individuals receive information from news agencies that are closer to their belief, confirmation bias is explicitly incorporated into the model. The proposed dynamics of cyber-social networks is adopted from DeGroot-Friedkin model, where the individual's opinion update mechanism is a convex combination of his innate opinion, his neighbors' opinions at the previous time step (obtained from the social network), and the opinions passed along by news agencies from cyber layer which he follows. The characteristics of the interdependent social and cyber networks are radically different here: the social network relies on trust and hence static while the news agencies are highly dynamic since they are weighted as a function of the distance between an individual state and the state of news agency to account for confirmation bias. The conditions for convergence of the aforementioned dynamics to a unique equilibrium are characterized. The estimation and exact computation of the steady-state values under non-linear and linear state-dependent weight functions are provided. Finally, the impact of polarization in the opinions of news agencies on the public opinion evolution is numerically analyzed in the context of the well-known Krackhardt's advice network.