Despite a growing number of powerful techniques for analyzing networks, network researchers often find themselves in need of simple and efficient ways to communicate results to a nonprofessional audience.
From the beginning, network analysis has been accompanied by more or less accurate attempts to visualize structure, mostly grounded on an intuitive understanding. There are many examples in the literature where simple geometric shapes (lines and circles) have been used to illustrate the underlying structure of datasets.
What we want to do is follow this tradition but in a systematic and automatic way by proposing a family of algorithms which try to grasp the core of the underlying structure. If they do exactly this, they are cheap in terms of computational demands.
How can we visualize network structures in a simple, systematic and parsimonious manner and check at the same time for errors which may result from such simplifications ?
After some general remarks about simplification and its problems from the perspective of model building, we will review different types of information that can be used to visualize network structures and propose how such information can be fitted into a constrained model space and how to handle errors.
A second part of this paper will analyze how the proposed procedure works for handmade toy examples containing simple structures and then proceed to compare results from the proposed algorithm with those of an extensively studied dataset.
Finally, we will apply the algorithm to complex 'real world datasets' and demonstrate its usefulness, when introducing a priori designs of the solution space.