We describe an empirical investigation into layout criteria that can help with the comprehension of Euler diagrams. Our work is intended to inform automatic Euler diagram layout research by confirming the importance of various Euler diagram aesthetic criteria. The three criteria under investigation were: smoothness, zone area equality and edge closeness. Subjects were asked to interpret diagrams with different combinations of levels for each of the criteria. Results for this investigation indicate that, within the parameters of the study, all three criteria are important for understanding Euler diagrams and we have a preliminary indication of the ordering of importance for the criteria. 1.

In this paper, we present a new graphical interface for traditional library environments, which allows the user to elaborate easily and efficiently new strategies in search processes. This tool is based on two linked interactive Euler diagram representations. The first one is an interactive representation of the structures composing the documentary kernel of the library. The user may navigate and select items, making their own understanding of the database content, structure and access. The second one is a set based visualization of the results of a composed query. This allows the user to validate his search context and to elaborate strategies to go through the results. The association of both interfaces generates a tool that allows the user to elaborate the main search strategies through graphical manipulations.

We introduce the concept of subdivision drawings of hypergraphs. In a subdivision drawing each vertex corresponds uniquely to a face of a planar subdivision and, for each hyperedge, the union of the faces corresponding to the vertices incident to that hyperedge is connected. Vertex-based Venn diagrams and concrete Euler diagrams are both subdivision drawings. In this paper we study two new types of subdivision drawings which are more general than concrete Euler diagrams and more restricted than vertex-based Venn diagrams. They allow us to draw more hypergraphs than the former while having better aesthetic properties than the latter.

Fig. 1. LineSets showing restaurant categories on a map (left), LineSets showing communities on a social network (right) Abstract — Computing and visualizing sets of elements and their relationships is one of the most common tasks one performs when analyzing and organizing large amounts of data. Common representations of sets such as convex or concave geometries can become cluttered and difficult to parse when these sets overlap in multiple or complex ways, e.g., when multiple elements belong to multiple sets. In this paper, we present a design study of a novel set visual representation, LineSets, consisting of a curve connecting all of the setʼs elements. Our approach to design the visualization differs from traditional methodology used by the InfoVis community. We first explored the potential of the visualization concept by running a controlled experiment comparing our design sketches to results from the state-of-the-art technique. Our results demonstrated that LineSets are advantageous for certain tasks when compared to concave shapes. We discuss an implementation of LineSets based on simple heuristics and present a study demonstrating that our generated curves do as well as human-drawn ones. Finally, we present two applications of our technique in the context of search tasks on a map and community analysis tasks in social networks. Index Terms — Set visualization, clustering, faceted data visualization, graph visualization. 1

Euler diagrams are the only diagrams that intuitively represent containment, intersection and exclusion of data, but none of the current automatic diagram layout techniques produce good layouts in a reasonable time. We adopt a force-directed approach to automatically layout aesthetically pleasing Euler diagrams in a relatively fast time. A Java prototype demonstrates our novel force model.

www.elsevier.com/locate/intcom Visualizing set concordance with permutation matrices and fan diagrams

Abstract. Using the notion of planarity and drawing for hypergraphs introduced respectively by Johnson and Pollak [9] and Mäkinen [14], we show in this paper that any hypergraph having less than nine hyperedges is vertex-planar and can be drawn in the edge standard and in the subset standard without edge crossing. Key words: hypergraphs, planarity, vertex-planarity, drawing in the edge standard, drawing in the subset standard, Euler diagrams 1