Drawing Graphs
Graphs are represented graphically by drawing a dot or circle for every vertex, and drawing an arc between two vertices if they are connected by an edge. If the graph is directed, the direction is indicated by drawing an arrow.
A graph drawing should not be confused with the graph itself (the abstract, non-visual structure) as there are several ways to structure the graph drawing. All that matters is which vertices are connected to which others by how many edges and not the exact layout. In practice it is often difficult to decide if two drawings represent the same graph. Depending on the problem domain some layouts may be better suited and easier to understand than others.
The pioneering work of W. T. Tutte was very influential in the subject of graph drawing. Among other achievements, he introduced the use of linear algebraic methods to obtain graph drawings.
Graph drawing also can be said to encompass problems that deal with the crossing number and its various generalizations. The crossing number of a graph is the minimum number of intersections between edges that a drawing of the graph in the plane must contain. For a planar graph, the crossing number is zero by definition.
Drawings on surfaces other than the plane are also studied.
Read more about this topic: Graph Theory
Famous quotes containing the word drawing:
“In the drawing room [of the Queen’s palace] hung a Venus and Cupid by Michaelangelo, in which, instead of a bit of drapery, the painter has placed Cupid’s foot between Venus’s thighs. Queen Caroline asked General Guise, an old connoisseur, if it was not a very fine piece? He replied “Madam, the painter was a fool, for he has placed the foot where the hand should be.””
—Horace Walpole (1717–1797)