The concept of graph layout

Graph layout is used in graphical user interfaces of applications that need to display graph models. To lay out a graph means to draw the graph so that an appropriate, readable representation is produced. Essentially, this involves determining the location of the nodes and the shape of the links. For some applications, the location of the nodes may already be known (for example, based on the geographical positions of the nodes). However, for other applications, the location is not known (a pure “logical” graph) or the known location, if used, would produce an unreadable drawing of the graph. In these cases, the location of the nodes must be computed.

What is meant by an “appropriate” drawing of a graph? In practical applications, it is often necessary for the graph drawing to observe certain quality criteria. These criteria may vary depending on the application field or on a given standard of representation. It is often difficult to tell what a good layout consists of. Each end user may have different, subjective criteria for qualifying a layout as “good”. However, one common goal exists behind all the criteria and standards: the drawing must be easy to understand and provide easy navigation through the complex structure of the graph.

To deal with the various needs of different applications, many classes of graph layout algorithms have been developed. A layout algorithm addresses one or more quality criteria, depending on the type of graph and the features of the algorithm, when laying out a graph.

The most common criteria are:

How can a layout algorithm meet each of these quality criteria and standards of representation? If you look at each individual criteria, some can be met quite easily, at least for some classes of graphs. For other classes, it may be quite difficult to produce a drawing that meets the criteria. For example, minimizing the number of link crossings is relatively simple for trees (that is, graphs without cycles). However, for general graphs, minimizing the number of link crossings is a mathematical NP-complete problem (that is, with all known algorithms, the time required to perform the layout grows very fast with the size of the graph).

Moreover, if you want to meet several criteria at the same time, an optimal solution may not exist with respect to each individual criteria because many of the criteria are mutually contradictory. Time-consuming trade-offs may be necessary. In addition, it is not a trivial task to assign weights to each criteria. Multicriteria optimization is, in most cases, too complex to implement and much too time-consuming. For these reasons, layout algorithms are often based on heuristics and may provide less than optimal solutions with respect to one or more of the criteria. Fortunately, in practical terms, the layout algorithms will still often provide reasonably readable drawings.

Layout algorithms can be employed in a variety of ways in the various applications in which they are used. The most common ways of using an algorithm are the following: