  One of the main subjects in the field of social networks is to quantify
conflict, disagreement, controversy, and polarization, and some quantitative
indicators have been developed to quantify these concepts. However, direct
computation of these indicators involves the operations of matrix inversion and
multiplication, which make it computationally infeasible for large-scale graphs
with millions of nodes. In this paper, by reducing the problem of computing
relevant quantities to evaluating $\ell_2$ norms of some vectors, we present a
nearly linear time algorithm to estimate all these quantities. Our algorithm is
based on the Laplacian solvers, and has a proved theoretical guarantee of error
for each quantity. We execute extensive numerical experiments on a variety of
real networks, which demonstrate that our approximation algorithm is efficient
and effective, scalable to large graphs having millions of nodes.
