## Section: New Results

### Graph Drawing

Participants : Dan Archambault, David Auber, Romain Bourqui, Paolo Simonetto.

#### Drawing large graphs

Drawing large graphs remain a difficult problem, as there are no obvious solution to produce a readable layout in reasonable time. We recently designed an algorithm to lay out a particular class of graphs emerging from real case studies, namely *quasi-trees* [12] . Protein interactions and internet mappings projects have shown the interest of designing dedicated tools for visualizing such a class of graphs. Our method addresses a challenging problem which consists in computing a layout of large graphs (up to hundred of thousands of nodes) that emphasizes their tree-like property in an efficient time, as shows Fig. 2 (which incidentally was the image used as front cover of the IEEE Information Visualization Conference proceedings in 2009).

In order to validate our approach, we compared our results on real data to those obtained by well known algorithms in term of computation times as well as drawings qualities.

#### Drawability of Euler diagrams

Visualization of taxonomies and other kinds of intersecting sets has recently become a focus of interest in the InfoVis community. The increasing number of application fields where cataloguing elements in strict hierarchies is no more enough. The need to take uncertainty and fuzzyness into account confirms the demand of visualisation methods that are able to handle these new structures. Euler diagrams, probably the most common and natural way of depicting intersecting sets, might provide the answer to these problems.

In Euler diagrams sets are identified by 2D regions enclosed by curves. The set intersections are then represented creating overlaps between the regions of the relative sets. This representation is so clear and intuitive that it is widely used in many different fields, also to introduce the mathematical concept of sets in elementary schools. Unfortunately, not all collection of sets admit a 2D Euler diagrams.

Euler representations are diagrams designed to extend the standard Euler ones, allowing to graphically depict even collection of intersecting sets otherwise undrawable [84] . They differ from standard Euler diagrams for the presence of visualisation patterns used when needed to overcome critical situations for standard Euler diagrams.

The automatic generation of these diagrams is possible through an algorithm first described in [83] and recently published in [9] and [15] .

These algorithms differ from other approaches already developed not only for its capability of dealing with every input instance, but also for the usage of techniques not yet adopted for Euler diagrams. Among others, the depiction of the countours using Bézier curves and the application of transparent coloured textures for improving the readability of the overlapped regions.

Fig. 3 shows the Euler representation calculated for a collection of films. Each film is intended as a set of actors, and overlaps are present when the same actor is in the cast of two or more films.

The films chosen for the pictures are a highly interconnected subset of the IMDb top 40 films. The Internet Movie Database (IMDb) is an online database of information related to films, actors and more generally to the cinema world. It reports a chart containing the top 250 films, ranked according to an overall vote calculated on the viewer rates. For sake of readability, each film in the picture contains only the first 20 actors in credit order.