  Can the topology of a network that consists of many particles interacting
with each other change in complexity when a phase transition occurs? The answer
to this question is particularly interesting to understand the nature of phase
transitions if the distinct phases do not break any symmetry, such as
topological phase transitions. Here we present a novel theoretical framework
established by complex network analysis for demonstrating that across a
transition point of the topological superconductors, the network space
experiences a homogeneous-heterogeneous transition invisible in real space.
This transition is nothing but related to the robustness of a network to random
failures. We suggest that the idea of the network robustness can be applied to
characterizing various phase transitions whether or not the symmetry is broken.
