  The investigation of social networks is often hindered by their size as such
networks often consist of at least thousands of vertices and edges. Hence, it
is of major interest to derive compact structures that represent important
connections of the original network. In this work, we derive such structures
with orometric methods that are originally designed to identify outstanding
mountain peaks and relationships between them. By adapting these methods to
social networks, it is possible to derive family trees of important vertices.
Our approach consists of two steps. We first apply a novel method for
discarding edges that stand for weak connections. This is done such that the
connectivity of the network is preserved. Then, we identify the important peaks
in the network and the key cols, i.e., the lower points that connect them. This
gives us a compact network that displays which peaks are connected through
which cols. Thus, a natural hierarchy on the peaks arises by the question which
higher peak comes behind the col, yielding to chains of peaks with increasing
heights. The resulting line-parent hierarchy displays dominance relations
between important vertices. We show that networks with hundreds or thousands of
edges can be condensed to a small set of vertices and key connections between
them.
