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

The Mont Blanc of Twitter: Identifying Hierarchies of Outstanding Peaks in Social Networks