K.: Visual analysis of network centralities

Centrality analysis determines the importance of vertices in a network based on their connectivity within the network structure. It is a widely used technique to analyse network-structured data. A particularly important task is the comparison of different centrality measures within one network. We present three methods for the exploration and comparison of centrality measures within a network: 3D parallel coordinates, orbit-based comparison and hierarchy-based comparison. There is a common underlying idea to all three methods: for each centrality measure the graph is copied and drawn in a separate 2D plane with vertex position dependent on centrality. These planes are then stacked into the third dimension so that the different centrality measures may be easily compared. Only the details of how centrality is mapped to vertex position are different in each method. For 3D parallel coordinates vertices are placed on vertical lines; for orbit-based comparison vertices are placed on concentric circles and for hierarchy-based comparison vertices are placed on horizontal lines. The second and third solutions make it particularly easy to track changing vertex-centrality values in the context of the underlying network structure. The usability of these methods is demonstrated on biological and social networks