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 simply 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.