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

Abstract

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.