  This paper studies topology inference, from agent states, of a directed
cyber-social network with opinion spreading dynamics model that explicitly
takes confirmation bias into account. The cyber-social network comprises a set
of partially connected directed network of agents at the social level, and a
set of information sources at the cyber layer. The necessary and sufficient
conditions for the existence of exact inference solution are characterized. A
method for exact inference, when it is possible, of entire network topology as
well as confirmation bias model parameters is proposed for the case where the
bias mentioned earlier follows a piece-wise linear model. The particular case
of no confirmation bias is analyzed in detail. For the setting where the model
of confirmation bias is unknown, an algorithm that approximates the network
topology, building on the exact inference method, is presented. This algorithm
can exactly infer the weighted communication from the neighbors to the
non-followers of information sources. Numerical simulations demonstrate the
effectiveness of the proposed methods for different scenarios.
