Area (graph drawing)
In graph drawing, the area used by a drawing is a commonly used way of measuring its quality.
Definition
For a drawing style in which the vertices are placed on the integer lattice, the area of the drawing may be defined as the area of the smallest axis-aligned bounding box of the drawing: that is, it the product of the largest difference in x-coordinates of two vertices with the largest difference in y-coordinates. For other drawing styles, in which vertices are placed more freely, the drawing may be scaled so that the closest pair of vertices have distance one from each other, after which the area can again be defined as the area of a smallest bounding box of a drawing. Alternatively, the area can be defined as the area of the convex hull of the drawing, again after appropriate scaling.
Polynomial bounds
For straight-line drawings of planar graphs with n vertices, the optimal worst-case bound on the area of a drawing is Θ(n2). The nested triangles graph requires this much area no matter how it is embedded, and several methods are known that can draw planar graphs with at most quadratic area.Binary trees, and trees of bounded degree more generally, have drawings with linear or near-linear area, depending on the drawing style. Every outerplanar graph has a straight-line outerplanar drawing with area subquadratic in its number of vertices, If bends or crossings are allowed, then outerplanar graphs have drawings with near-linear area. However, drawing series-parallel graphs requires an area larger than n by a superpolylogarithmic factor, even if edges can be drawn as polylines.
Area chart
An area chart or area graph displays graphically quantitive data. It is based on the line chart. The area between axis and line are commonly emphasized with colors, textures and hatchings. Commonly one compares with an area chart two or more quantities.
History
William Playfair is usually credited with inventing the area charts as well as the line, bar, and pie charts. His book The Commercial and Political Atlas, published in 1786, contained a number of time-series graphs, including Interest of the National Debt from the Revolution and Chart of all the Imports and Exports to and from England from the Year 1700 to 1782 that are often described as the first area charts in history.
Common uses
Area charts are used to represent cumulated totals using numbers or percentages (stacked area charts in this case) over time. Use the area chart for showing trends over time among related attributes. The area chart is like the plot chart except that the area below the plotted line is filled in with color to indicate volume.
