  We say that a population is perfectly polarized when divided in two groups of
the same size and opposite opinions. In this paper, we propose a methodology to
study and measure the emergence of polarization from social interactions. We
begin by proposing a model to estimate opinions in which a minority of
influential individuals propagate their opinions through a social network. The
result of the model is an opinion probability density function. Next, we
propose an index to quantify the extent to which the resulting distribution is
polarized. Finally, we apply the proposed methodology to a Twitter conversation
about the late Venezuelan president, Hugo Ch\'avez, finding a good agreement
between our results and offline data. Hence, we show that our methodology can
detect different degrees of polarization, depending on the structure of the
network.
