Throughout this paper we have followed the idea of enhancing communication of network results by approaching the complexity of visualizations. We have proposed an algorithm and shown that it finds cliques and clusters of cohesion for simple structures and also for more complex datasets.
Due to the fact that this algorithm uses a precedence criterion to attach errors to structurally less important elements, it gives us the opportunity to work with highly restricted solution spaces, while ensuring that the visualizations grasp the most important parts of the underlying structure.
The formal procedure itself can be applied to any distance-type information derived from network data. These data may differ in the richness of information they provide, moving the focus of visualization from direct links only to the possible consequences of indirect links. Therefore the road to more theory-guided centrality measures in the future is open.
Moving to large and more complex networks, we have demonstrated that the outlined procedure can be used as a building block to approach networks of networks: we have used additional a prori information to assign nodes to several shapes. The algorithm itself can handle the information even in these cases. It tries to use the empirical information on the basis of the a priori constraints to fit the data.
As a priori designs affect the distances in the model space and thus the evaluation of the minimal positions, more knowledge and experience is needed to fully exploit the range of alternative designs.
Visualizations need not to be perfect in terms of fit but fulfill their purpose when they guide the audience to the most important characteristics of the underlying subject. Nevertheless thinking in terms of a sequential approach from simple illustrations to a parsimonious model, we would benefit from more guidance on how to find the ideal balance between simplicity and fit. As this point we think of rank correlations between the model and empirical distances, but it is still unclear whether they can serve to sort out the best means by which we can expect to find this balance: by increasing the degrees of freedom or by using alternative designs. If we had such criteria, they could also help us to choose among a variety of alternative designs.