  We suggest an approach to study hierarchy, especially hidden one, of complex
networks based on the analysis of their vulnerability. Two quantities are
proposed as a measure of network hierarchy. The first one is the system
vulnerability V. We show that being quite suitable for regular networks this
characteristic does not allow one to estimate the hierarchy of large random
networks. The second quantity is a relative variance h of the system
vulnerability that allows us to characterize a "natural" hierarchy level of
random networks. We find that hierarchical properties of random networks depend
crucially on a ratio between the number of nodes and the number of edges. We
note that any graph with a transitive isometry group action (i.e. an absolutely
symmetric graph) is not hierarchical. Breaking such a symmetry leads to
appearance of hierarchy.
