The Wolfram Language provides functions for the aesthetic drawing of graphs. Algorithms implemented include spring embedding, spring-electrical embedding, high-dimensional embedding, radial drawing, random embedding, circular embedding, and spiral embedding. In addition, algorithms for layered/hierarchical drawing of directed graphs as well as for the drawing of trees are available. These algorithms are implemented via four functions: GraphPlot, GraphPlot3D, LayeredGraphPlot, and TreePlot.

GraphPlot and GraphPlot3D are suitable for straight line drawing of general graphs. LayeredGraphPlot attempts to draw the vertices of a graph in a series of layers; therefore it is most suitable for applications such as the drawing of flow charts. TreePlot is particularly useful for drawing trees or tree-like graphs. These functions are designed to work efficiently for very large graphs.

In these functions, a graph is represented either by a list of rules of the form {v_i1->v_j1,…}, where v_i1 and v_j1 are vertices, or by the adjacency matrix of the graph.

A graph consists of a set of vertices (also called nodes) and a set of edges . Two vertices and form an edge of the graph if .

If implies that , then is an undirected graph. Otherwise it is a directed graph. The former can be drawn using line segments, while the latter can be drawn with arrows. In an undirected graph, it is often convenient to denote that an edge exists between and with the notation