  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.
