  The adaptive social learning paradigm helps model how networked agents are
able to form opinions on a state of nature and track its drifts in a changing
environment. In this framework, the agents repeatedly update their beliefs
based on private observations and exchange the beliefs with their neighbors. In
this work, it is shown how the sequence of publicly exchanged beliefs over time
allows users to discover rich information about the underlying network topology
and about the flow of information over the graph. In particular, it is shown
that it is possible (i) to identify the influence of each individual agent to
the objective of truth learning, (ii) to discover how well-informed each agent
is, (iii) to quantify the pairwise influences between agents, and (iv) to learn
the underlying network topology. The algorithm derived herein is also able to
work under non-stationary environments where either the true state of nature or
the graph topology are allowed to drift over time. We apply the proposed
algorithm to different subnetworks of Twitter users, and identify the most
influential and central agents by using their public tweets (posts).
