A graph drawing is a representation of a graph in a geometric space in which distinct vertices are represented by distinct points and each graph edge is represented by a curve joining the points corresponding to its endpoints. A general graph drawing may have crossings between edges that do not share an endpoint. This distinguishes a graph drawing from a graph embedding, in which edges intersect only at common endpoints.
The abstract graph specifies which pairs of vertices are adjacent, but not the positions of the points or the shapes of the curves in a drawing. Consequently, the same graph can have many different graph drawings. Drawings are usually made in the plane, although drawings in three or more dimensions are also used.
Special types of graph drawings impose additional geometric conditions. In a circular drawing, all vertices lie on a circle; in a straight line drawing, every edge is a line segment; and in an integral drawing, edge lengths are integers. A drawing in the plane whose edges meet only at common endpoints is a planar graph embedding. Graph drawing algorithms seek informative and legible layouts using criteria such as the numbers of crossings and bends, drawing area, edge lengths, angular resolution, and symmetry (Di Battista et al. 1998; Tamassia 2000).
Graphs can be drawn in the Wolfram Language using Graph[
...
], with layouts specified using the option GraphLayout.
