Persistent Homology Guided Force-Directed Graph Layouts

Improved Force-Directed Layouts

Techniques for drawing graphs based on force-directed placement and virtual physical models have proven surprisingly successful in producing good layouts of undirected graphs. Aspects of symmetry, structure, clustering and reasonable vertex distribution arise from initial, formless clouds of points. However, when nodes must be labeled and point vertices are replaced by non-point vertices, simpl...

User Control of Force-directed Layouts

Force-directed layouts are typically used for minimizing overlaps in node-link graphs. This can make it easier to interpret and derive meaning from the resulting visualization. Once such a layout is put in motion, however, the person interacting with it has little control over the “final” layout. This paper describes an approach that puts even inexperienced users in charge of force-directed lay...

Persistent Homology Over Directed Acyclic Graphs

We define persistent homology groups over any set of spaces which have inclusions defined so that the underlying graph between the spaces is directed and acyclic. This method simultaneously generalizes standard persistent homology, zigzag persistence and multidimensional persistence to arbitrary directed acyclic graphs, and it also allows the study of arbitrary families of topological spaces or...

Persistent Path Homology of Directed Networks

Graphael: A System for Generalized Force-Directed Layouts

The graphael system implements several classic force-directed layout methods, as well as several novel layout methods for non-Euclidean geometries, including hyperbolic and spherical. The system can handle large graphs, using multi-scale variations of the force-directed methods. Finally, the system can layout and visualize graphs that evolve though time, using static views, animation, and morph...