  In recent years, the theory and application of complex networks have been
quickly developing in a markable way due to the increasing amount of data from
real systems and to the fruitful application of powerful methods used in
statistical physics. Many important characteristics of social or biological
systems can be described by the study of their underlying structure of
interactions. Hierarchy is one of these features that can be formulated in the
language of networks. In this paper we present some (qualitative) analytic
results on the hierarchical properties of random network models with zero
correlations and also investigate, mainly numerically, the effects of different
type of correlations. The behavior of hierarchy is different in the absence and
the presence of the giant components. We show that the hierarchical structure
can be drastically different if there are one-point correlations in the
network. We also show numerical results suggesting that hierarchy does not
change monotonously with the correlations and there is an optimal level of
non-zero correlations maximizing the level of hierarchy.
