  We present a novel theoretical framework established by complex network
analysis for understanding the phase transition beyond the Landau symmetry
breaking paradigm. In this paper we take a two-dimensional metal-insulator
transition driven by electron correlations for example. Passing through the
transition point, we find a hidden symmetry broken in the network space, which
is invisible in real space. This symmetry is nothing but a kind of robustness
of the network to random failures. We then show that a network quantity,
small-worldness, is capable of identifying the phase transition with/without
any symmetry breaking in the real space and behaving as a new order parameter
in the network space. We demonstrate that whether or not the symmetry is broken
in real space a variety of phase transitions in condensed matters can be
characterized by the hidden symmetry breaking in the weighted network, that is
to say, a decline in network robustness.
