Graph drawing

Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, and bioinformatics.[1]

A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph.[2] In the abstract, all that matters is which pairs vertices are connected by edges. In the concrete, however, the arrangement of these vertices and edges within a drawing affects its understandability, usability, fabrication cost, and aesthetics.[3] The problem gets worse, if the graph changes over time by adding and deleting edges (dynamic graph drawing) and the goal is to preserve the user's mental map[4].

Contents

Graphical conventions

Graphs are frequently drawn as node-link diagrams in which the vertices are represented as disks or boxes and the edges are represented as line segments, polylines, or curves in the Euclidean plane.[3]

In the case of directed graphs, arrowheads form a commonly-used graphical convention to show their orientation;[2] however, user studies have shown that other conventions such as tapering provide this information more effectively.[5]

Alternative conventions to node-link diagrams include adjacency representations such as circle packings, in which vertices are represented by disjoint regions in the plane and edges are represented by adjacencies between regions; intersection representations in which vertices are represented by non-disjoint geometric objects and edges are represented by their intersections; visibility representations in which vertices are represented by regions in the plane and edges are represented by regions that have an unobstructed line of sight to each other; confluent drawings, in which edges are represented as smooth curves within mathematical train tracks; and visualizations of the adjacency matrix of the graph.

Quality measures

Many different quality measures have been defined for graph drawings, in an attempt to find objective means of evaluating their aesthetics and usability.[6] In addition to guiding the choice between different layout methods for the same graph, some layout methods attempt to directly optimize these measures.

Layout methods

There are many different graph layout strategies:

Application-specific graph drawings

Graphs and graph drawings arising in other areas of application include

In addition, the placement and routing steps of electronic design automation are similar in many ways to graph drawing, and the graph drawing literature includes several results borrowed from the EDA literature. However, these problems also differ in several important ways: for instance, in EDA, area minimization and signal length are more important than aesthetics, and the routing problem in EDA may have more than two terminals per net while the analogous problem in graph drawing generally only involves pairs of vertices for each edge.

Software

Software, systems, and providers of systems for drawing graphs include:

Notes

  1. ^ Di Battista et al. (1994), pp. vii–viii; Herman, Melançon & Marshall (2000), Section 1.1, "Typical Application Areas".
  2. ^ a b Di Battista et al. (1994), p. 6.
  3. ^ a b Di Battista et al. (1994), p. viii.
  4. ^ Misue et al. (1995)
  5. ^ Holten & van Wijk (2009); Holten et al. (2011).
  6. ^ Di Battista et al. (1994), Section 2.1.2, Aesthetics, pp. 14–16; Purchase, Cohen & James (1997).
  7. ^ Di Battista et al. (1994), p 14.
  8. ^ Di Battista et al. (1994), p. 16.
  9. ^ Formann et al. (1993).
  10. ^ Di Battista et al. (1994), Section 2.7, "The Force-Directed Approach", pp. 29–30, and Chapter 10, "Force-Directed Methods", pp. 303–326.
  11. ^ Beckman (1994); Koren (2005).
  12. ^ Di Battista et al. (1994), Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; (Eiglsperger, Fekete & Klau 2001).
  13. ^ Herman, Melançon & Marshall (2000), Section 2.2, "Traditional Layout – An Overview".
  14. ^ Sugiyama, Tagawa & Toda (1981); Bastert & Matuszewski (2001); Di Battista et al. (1994), Chapter 9, "Layered Drawings of Digraphs", pp. 265–302.
  15. ^ Doğrusöz, Madden & Madden (1997).
  16. ^ Scott (2000).
  17. ^ Di Battista et al. (1994), pp. 15-16, and Chapter 6, "Flow and Upward Planarity", pp. 171–214; Freese (2004).
  18. ^ Zapponi (2003).
  19. ^ Anderson & Head (2006).
  20. ^ "Graphviz and Dynagraph – Static and Dynamic Graph Drawing Tools", by John Ellson, Emden R. Gansner, Eleftherios Koutsofios, Stephen C. North, and Gordon Woodhull, in Jünger & Mutzel (2004).
  21. ^ "yFiles – Visualization and Automatic Layout of Graphs", by Roland Wiese, Markus Eiglsperger, and Michael Kaufmann, in Jünger & Mutzel (2004).
  22. ^ Nachmanson, Robertson & Lee (2008).
  23. ^ Madden et al. (1996).
  24. ^ "Tulip – A Huge Graph Visualization Framework", by David Auber, in Jünger & Mutzel (2004).

References

External links