  The presence of hierarchy in many real-world networks is not yet fully
explained. Complex interaction networks are often coarse-grain models of vast
modular networks, where tightly connected subgraphs are agglomerated into nodes
for simplicity of representation and feasibility of analysis. The emergence of
hierarchy in growing complex networks may stem from one particular property of
these ignored subgraphs: their graph conductance. Being a quantification of the
main bottleneck of flow on the subgraph, all such subgraphs will then have a
specific structural limitation associated with this scalar value. This supports
the consideration of heterogeneous degree restrictions on a randomly growing
network for which a hidden variable model is proposed based on the basic
\textit{rich-get-richer} scheme. Such node degree restrictions are drawn from
various probability distributions, and it is shown that restriction generally
leads to increased measures of hierarchy, while altering the tail of the degree
distribution. Thus, a general mechanism is provided whereby inherent
limitations lead to hierarchical self-organization.
