A key argument for modeling knowledge in ontologies is the easy re-use and re-engineering of the knowledge. However, current ontology engineering tools provide only basic functionalities for analyzing ontologies. Since ontologies can be considered as graphs, graph analysis techniques are a suitable answer for this need. Graph analysis has been performed by sociologists for over 60 years, and resulted in the vivid research area of Social Network Analysis (SNA). While social network structures currently receive high attention in the Semantic Web community, there are only very few SNA applications, and virtually none for analyzing the structure of ontologies. We illustrate the benefits of applying SNA to ontologies and the Semantic Web, and discuss which research topics arise on the edge between the two areas. In particular, we discuss how different notions of centrality describe the core content and structure of an ontology. From the rather simple notion of degree centrality over betweenness centrality to the more complex eigenvector centrality, we illustrate the insights these measures provide on two ontologies, which are different in purpose, scope, and size.