Interactive design and visualization of N-ary relationships

Graph and network visualization is a well-researched area. However, graphs are limited in that by definition they are designed to encode pairwise relationships between the nodes in the graph. In this paper, we strive for visualization of datasets that contain not only binary relationships between the nodes, but also higher-cardinality relationships (ternary, quaternary, quinary, senary, etc). While such higher-cardinality relationships can be treated as cliques (a complete graph of N nodes), visualization of cliques using graph visualization can lead to unnecessary visual cluttering due to all the pairwise edges inside each clique. In this paper, we develop a visualization for data that have relationships with cardinalities higher than two. By representing each N-ary relationship as an N-sided polygon, we turn the problem of visualizing such data sets into that of visualizing a two-dimensional complex, i.e. nodes, edges, and polygonal faces. This greatly reduces the number of edges needed to represent a clique and makes them as well as their cardinalities more easily recognized. We develop a set of principles that measures the effectiveness of the visualization for two-dimensional complexes. Furthermore, we formulate our strategy with which the positions of the nodes in the complex and the orderings of the nodes inside each clique in the complex can be optimized. Furthermore, we allow the user to further improve the layout by moving a node or a polygon in 3D as well as changing the order of the nodes in a polygon. To demonstrate the effectiveness of our technique and system, we apply them to a social network and a gene dataset.