  The properties of q-dependent cross-correlation matrices of stock market have
been analyzed by using the random matrix theory and complex network. The
correlation structures of the fluctuations at different magnitudes have unique
properties. The cross-correlations among small fluctuations are much stronger
than those among large fluctuations. The large and small fluctuations are
dominated by different groups of stocks. We use complex network representation
to study these q-dependent matrices and discover some new identities. By
utilizing those q-dependent correlation-based networks, we are able to
construct some portfolio by those most independent stocks which consistently
perform the best. The optimal multifractal order for portfolio optimization is
approximately $q=2$. These results have deepened our understanding about the
collective behaviors of the complex financial system.
