In a complement graph, the two vertices, which are formed after reflection of the vertices of the actual graph, are adjacent only if they are not adjacent in the actual graph. In order to make a complement graph H of an actual graph G, one has to fill in all the absent edges and remove the edges of the graph G. It is a highly challenging and technical graph to create which requires a lot of practice and skill, as well as a deep understanding of mathematical conceptions.

There are various kinds of complement graphs like claw free graphs, complete graphs, and self complementary graph. These differ significantly and must be drawn with precision and accuracy in order to create the perfect graph.

Complement graphs must be labeled correctly and the axes must be clearly defined as well. Complement graphs are extremely useful in certain specific areas, and thus, they must be drawn with care and accuracy.

Complement graphs are not the set complement of a graph. They should not be mistaken as such as their properties are very different from those of set complement.

Complement graphs are not easily accessible as they are complex. However, on a deeper understanding of graph theory, complement graphs can be put to a lot of use.

Example of a Complement Graph.

Sample Complement Graph

Dual graphs are those, where for a planar graph G, the graph has a vertex for each plane region of G. Dual graphs are highly complex mathematical concepts which require skill and considerable study in order to grasp them. Self dual graphs are also a subgroup of dual graphs. Some their important properties are as follows:

The dual graph H for a planar graph G must be drawn in a way that G is also the dual graph of H. This makes dual graphs symmetric and this is why they have been given the name of dual graphs.

Dual graphs are often used to represent RNA. This is an interesting use of dual graphs which is inter-generic. Biological functions are also often represented with the help of dual graphs.

Dual graphs are highly technical and thus they are only used for academic purposes or in very specialized fields. They should be correctly written keeping in mind the complex mathematical equations involving planar graphs.

Dual graphs of planar graphs are also known as planar multigraphs. Combinatorial dual graphs are also part of this group of specialized graphs. Dual graphs must be labeled correctly; otherwise they are ambiguous and meaningless.

Example of a Dual Graph.

Sample Dual Graph

Interactive graphs are those which facilitate greater viewer interaction with the data that has been plotted on a graph. They require special plug-ins and can be downloaded from the internet as well. The advantages of interactive graphs are obvious and they have gained acceptance across all spheres. Such graphs not only convey information, but also allow the reader to play with it, and make changes suiting his own requirements.

Interactive graphs are also known as flash charts. They allow the reader to foresee developments in the graph by plotting different points than the ones that are already part of the graph. All kinds of graphs like bar graphs, pie charts, cosmographs and so on are available in their interactive versions.

They are often used in offices and they make a particularly impressive device to use in board meetings and such. The demonstrator can use the interactive graph to convey more information and the audience becomes a participant in this dynamic process. They offer greater clarity than ordinary graphs and thus interactive graphs are used commonly.

Interactive graphs are available in both 2D and 3D format, thus offering a wide range of choices to the audience. They are technically difficult to create and require some amount of practice.

Example of a Interactive Graph.

Sample Interactive Graphs

A histogram is the graphical representation of numerical data. It is a very common type of graph and consists of an x and a y axis. The representation of numerical data on a graph paper is a better way of conveying the import of the data. The term was coined by Karl Pearson and histograms usually use bar graphs in their representations. A histogram has both advantages and disadvantages and they must be constructed with care and accuracy.

Histograms generally represent how frequently an event occurs and the time in which they occur. This is the primary kind of data that histograms deal with, and therein lies its importance. For example, a histogram may convey how frequently injuries occur among a certain group of people, and the times at which they occur.

The time is labeled on the x axis and the frequency on the y. This makes it easier to represent numerical data visually. By doing so, histograms make a greater impact than the plain numerical presentation of the same data.

Histograms are fairly simple to understand. However, they do provide valuable inputs about the data and the changes observed. A histogram can be constructed with relative ease making it one of the most popular graphs.

Example of a Histogram.

Histogram

Scatter plots are graphs which are composed of points and use a Cartesian system. They represent the variable values for a set of data. Scatter plots are also known as scattergrams, scatter diagrams, scatter charts and so on.

Each point which makes up the scatter plot consists of one variable that makes up the value on the horizontal axis or x axis and the other variable that makes up the value on the vertical y axis. Scatter plots are commonly used and they require some amount of technical skill in understanding.

The first variable is plotted on the x axis and the second on the y axis. Thus, this graph is built on two variables making it flexible and adaptable to a wide range of data. Scatter graphs can be shaded and color coordinated in order to ensure that the information comes across clearly and in the correct manner.

They are also known as XY graphs and are used to determine cause and effect. The use of the double variable in the scatter graph lends to creating this particular use.

Best fit or trend lines demonstrate the ideal relationship between the two variables. They should leave the same number of unconnected dots on either side of the main line, and as many dots as possible should be joined.

Example of a Scatter Plot.

Sample Scatter Plot

A parabola is a conic section, with a focus and a directrix. The representation of a parabola on a graph is called a parabolic graph. Parabola graphs are commonly used in mathematics and physics and they are also extremely useful in a number of other fields. They are also used extensively in engineering and design to calculate values and so on.

The parabola crosses the x axis and the y axis. They are applied in a number of areas from the reflection of headlights to the design of ballistic missiles. Hence, the importance of graphing parabolas is immense and it must be done correctly following the mathematical equations given.

Parabola graphs are technical in nature and hence, they can only be drawn following an understanding of the mathematical concepts of the graph and the parabola. Thus, their uses are technical as well.

The occurrence of parabolas in daily life is immense, and thus, the need for representing numerical data visually also increases. However, for laymen, the understanding of parabola graphs is dependent on their understanding of parabolas as a mathematical concept.

The quadratic equation that forms the parabola must first be solved and then the respective points plotted. This has to be done with accuracy in order to create a correct graphical rendition.

Example of a Parabola Graph.

Sample Parabola Graph

Cosmographs are a kind of graph resembling pie charts, with significant differences as well. They are not as numerically oriented as pie charts and they are usually used in order to represent finances. Cosmographs have their advantages as well as their disadvantages and yet, they are used quite commonly.

Cosmographs are often used by government agencies to represent the amount of funds they applied to various projects. In such representations, the data which forms the whole, like the amount of funds allocated by the government, are represented on the left of the cosmograph, whereas the data that represents a part, like the amount of funds allocated for specific projects by the government, are mentioned on the right hand side of the cosmograph.

Cosmographs can also be used to represent fractions and percentages. They are also often used to highlight differences between various geographical regions. Such cosmographs can also be distinguished using various colors and patterns to make the differences clear and prominent.

Most cosmographs use the input-output model and this is the primary manner in which they have proved to be extremely useful. Cosmographs are technically difficult and challenging, and require technical mastery. Hence, while an important kind of graph, cosmographs are mainly restricted to specific uses only.

Example of a cosmographs.

Cosmograph

Pictographs are graphs where pictures or symbols are used to represent the various points and data on the graph, along with a key. They are usually used in schools to impart basic education in graphs to students who are just beginning to get a grasp of graphs. However, they are challenging and pictographs need some amount of technical expertise as well.

The most crucial element of a pictograph is the key which will provide a list of all the pictures or symbols used and their corresponding data. A pictograph is incomplete without the key and special attention must be provided to ensure that the key is absolutely accurate and spot on.

Pictographs are easy to understand as they use pictures in order to convey the basic information. However, they do have a tendency to become clumsy and overcrowded and hence, care should be taken to create a neat and compact pictograph.

Pictographs are also not very accurate. For example, in a pictograph if the image of one orange represents ten oranges on the graph, then representing one or two oranges becomes extremely difficult. Thus they are not flexible and hence, pictographs are not commonly used for different kinds of graphs.

Example of a Pictographs.

Sample Pictographs

Linear graphs are graphical representations of linear equations. They are one of the most common forms of graphs which are plotted for a wide variety of purposes. Linear graphs must be plotted in a slope-intercept form within rectangular coordinates. Once the technical aspect of graph plotting is understood, plotting linear graphs becomes easy and convenient.

A linear graph is a straight line graph whose slope is the equation. A linear graph helps depict a linear relationship by means of which when one value goes up, the other makes a change by the same amount every time.

Linear graphs should be titled clearly. The axes must be clearly labeled and a key with the value of each unit must be mentioned. This is the most important part of a linear graph. If the ratio and the key are not mentioned correctly, linear graphs will yield faulty results.

The advantage of a linear graph over a linear equation is that the former is much more vivid and conveys information in a superior manner. Even for those who are unable to solve linear equations, a linear graph can convey information easily.

Linear graphs are flexible and adaptable. Once the data can be resolved into a linear equation, and the slope is calculated, forming linear equation becomes simple enough.

Example of a Linear Graph.

Sample Linear Graph