Displaying Centrality of a Network using Orbital Layout

Network analysis uses centralities as a method to order the actors and the links between them according to their importance based on the structural properties of the given network. In mathematical terms a network can be modelled as an instance of the abstract object graph, where the actors of the network are vertices and the links are represented by edges. An intuitive form of visualization of a centrality is placing its vertices on concentric circles. Vertices with a higher centrality value are situated close to the center. With decreasing importance vertices are placed on circles further away from the center. We extended the already existing radial and circular layout and defined the term orbital layout, where both interorbit and intraorbit edges are allowed. To be able to produce a conceptional drawing, visual complexity needs to be reduced. The first approach is based on crossing minimization to achieve a good readability. Two heuristics are presented, the first one is based on string matching and the second heuristic is an extension of the radial sifting algorithm to orbital layout. A second idea, based on planarization, is to first planarize the input graph and then reinsert the deleted edges. We introduce three greedy algorithms based on edge centrality to compute maximal planar subgraphs in circular, radial and orbital layout as the original problem, the determination of the maximum planar subgraph is NP-hard for all three layouts.