  Hierarchical organisation is a prevalent feature of many complex networks
appearing in nature and society. A relating interesting, yet less studied
question is how does a hierarchical network evolve over time? Here we take a
data driven approach and examine the time evolution of the network between the
Medical Subject Headings (MeSH) provided by the National Center for
Biotechnology Information (NCBI, part of the U. S. National Library of
Medicine). The network between the MeSH terms is organised into 16 different,
yearly updated hierarchies such as "Anatomy", "Diseases", "Chemicals and
Drugs", etc. The natural representation of these hierarchies is given by
directed acyclic graphs, composed of links pointing from nodes higher in the
hierarchy towards nodes in lower levels. Due to the yearly updates, the
structure of these networks is subject to constant evolution: new MeSH terms
can appear, terms becoming obsolete can be deleted or be merged with other
terms, and also already existing parts of the network may be rewired. We
examine various statistical properties of the time evolution, with a special
focus on the attachment and detachment mechanisms of the links, and find a few
general features that are characteristic for all MeSH hierarchies. According to
the results, the hierarchies investigated display an interesting interplay
between non-uniform preference with respect to multiple different topological
and hierarchical properties.
