  Extraction of interaction networks from multi-variate time-series is one of
the topics of broad interest in complex systems. Although this method has a
wide range of applications, most of the previous analyses have focused on the
pairwise relations. Here we establish the potential of such a method to elicit
aggregated behavior of the system by making a connection with the concepts from
percolation theory. We study the dynamical interaction networks of a financial
market extracted from the correlation network of indices, and build a weighted
network. In correspondence with the percolation model, we find that away from
financial crises the interaction network behaves like a critical random network
of Erd\H{o}s-R\'{e}nyi, while close to a financial crisis, our model deviates
from the critical random network and behaves differently at different size
scales. We perform further analysis to clarify that our observation is not a
simple consequence of the growth in correlations over the crises.
