Graphs Examples

Graphs are widely used in different industries as a Data Interpretation medium. They display the data in a simple, friendly manner so the audience can easily comprehend the information. It is also proven that people quickly grasp the visually presented data in graphs compared to when presented as a text or in a data table (numerically).

People often compose detailed data graphs to interpret them more efficiently in a graphical format than a numerical table. Let's quickly discover the various industries where Graphs are commonly used:

Application of Graphs

1. Computer Science or IT: Graphs play a significant role in representing computer data, communication networks, data organization, data structures, computational devices, etc. Therefore, developers have introduced various types of graphs in the computer data structure.
2. Physics and Chemistry: Graphs are used to less complicate the Science concepts, especially the study of molecules in chemistry and physics.
3. Social Science and Economic: Numbers are easily represented with Graphs. Therefore, commonly used in Social Science and economics.
4. Mathematics and Statistic: Graph theory is helpful in data tables, geometry, and some specified parts of topology, unlike the knot theory.
5. Biology: In this, Graph conservation energies and represent other biological reactions in a straightforward manner.

Graphs used in Mathematics, Science and Social Science

In general subjects, unlike Mathematics, Biology, and Social Science, a graph can be defined as a pictorial representation or a diagram that interprets data or values in an organized manner. The features on the graph usually signify the relationship between two or more entities.

Types of Graphs

1. Pie Chart or Circle Graph

As the name suggests, a pie chart or a circle graph resembles a circle shape. The circle is further split into sections that look like the slices of a pie. As it resembles a pie, therefore it is called a Pie Graph.

2. Bar Graph

A bar graph displays the categorical information using rectangular bars with heights or lengths relative to the data they signify. The graph can represent the data in either numerical or words format, where the bars can either be in vertical or horizontal layout.

3. Histogram Graph

A bar graph where the values are displayed in different heights of bars is defined as a histogram graph.

4. Line Graph

A line graph represents the values as a point charted on the graph. Later, these points the joined, and they form a line. Therefore, it is known as a Line Graph.

5. Flowcharts

Flowcharts represents a schematic workflow or a specified process. Different enterprises take advantage of flowcharts to present the various phases of a project.

Data Structure Graph- Examples & Types

In Computer Science, the graph is defined as a picturesque model of a set of objects (usually vertex and edges) where they are connected via links.

The interrelated objects are denoted by points known as vertices, and the links that join the pair of objects in the graph's vertices are known as edges.

G = (V, E)

Where,

G stands for Graph

V stands for Vertex

E stands for Edges

The graphs contain a set of vertices and set of edges that are represented by the following:

Vertices=> V = {V1, V2, . .}

Edges=> E = {E1, E2, . . .}

• Two vertices (Vm, Vn) are termed as adjacent if there exist an edge (Ek) which is connected to both the vertex i.e., Vi and Vj.
• In the above case Vm and Vn are also known as end points and the edge Ek is called a connect/joint of Vm and Vn.

Types & Examples

1. Finite Graphs

A finite Graph is defined as a graph that contains the finite figure of vertices (Vi) and a finite number of edges (Ej). The graphic representation of a finite graph is given below:

2. Infinite Graph

An infinite graph is defined as a graph that contains an infinite figure of vertices (Vn) and an infinite number of edges (En). The graphic representation of an infinite graph is as given below:

3. Trivial Graph

A graph is defined as a Trivial Graph if a finite graph includes only one vertex (V1) and no edges.

4. Simple Graph

A Simple graph is defined as a graph containing a pair of vertices (Vm, Vn), and there exists only one edge (e) in between them. The real-life example of a Simple Graph is the concept of railway tracks connecting with different cities.

5. Multi Graph

A Multi Graph is defined as a Multi Graph that contains some parallel edges but doesn't include any self-loop. The real-life example of a Multi Graph is a Road Map.

Two new concepts introduced in Multi-graph are mentioned below:

• Parallel Edges: An Edge in a graph is referred to as a Parallel Edge if it contains many roots but a single destination, unlike if any two vertices of the graph are linked with more than one edge.
• Loop: Loop or self-loop is referred to as a term where an edge of a graph connects a vertex to itself.

6. Null Graph

Any graph of order n and size zero (0) is known as Null Graph. They can have two or more 'n' number of vertices but no edge.

7. Complete Graph

Completed graph is the upgraded version of a simple graph that contains the 'n' number of vertices where the degree of each vertex is n-1, i.e., each vertex is connected with n-1 edges. Another name of this graph is Full Graph.

8. Pseudo Graph

The pseudo graph is defined as a graph that contains a self-loop and multiple edges.

9. Regular Graph

If all the vertices of a simple graph are of equal size, that graph is known as Regular Graph. Therefore, all complete graphs are regular graphs, but vice versa is not feasible.

10. Bipartite Graph

A Bipartite Graph is referred to a graph(G) where the vertex set V(G) can be split into two (bi) non-empty disjoint subsets, i.e., V1(G) and V2(G), so that the edge of E(G) has its one end in the vertex (V1(G)) and another end in the vertex (V2(G)). As you can refer to the below figure, where

• V1(vertex 1)={V5, V4, V3}, V1 is partitioning into three non-empty disjoint subsets namely V5, V4, V3.
• V2(vertex 2)={V1, V2}, V2 is partitioning into two non-empty disjoint subsets namely V1, V2

11. Labelled Graph

Labelled Graphs are defined as the Graphs whose all vertices and edges are assigned with some information that possibly could be a name, data, or weight. Another name of this graph is Weighted Graph.

12. Digraph Graph

A Digraph graph id defined as a Graph (G) with a mapping factor (f) wherein each and every edge (e) maps with the ordered pair of vertices (Vm, Vn). The Digraph graph is also known as Directed Graph.

Ordered pair (Vm, Vn) is a pair of vertexes where an edge between two vertexes Vm and Vn is represented with an arrow pointed from Vm to Vn.

In the above diagram, you will notice the following connection between Edges and vertices:

• E1 = (V1, V2)
• E1 = (V2, V3)
• E1 = (V2, V4)

13. Subgraph

A graph (G) = (V1, e1) is said to be a subgraph of a graph G(V, e) if the vertex V1(G) of Graph (G) is a subset of vertex V(G) and the edge e1(G) is a subset of edge e(G) in such a manner that each edge of G1 has identical end vertices that are present in Graph (G).

14. Connected or Disconnected Graph

Any graph is defined as a Connected Graph if the Graph (G) contains any pair of vertices (Vm, Vn), which is accessible to both the vertices in the Graph (G) and it should contain at least one path between the pairs of vertices (Vm, Vn). If the above condition is not matched, the graph is said to be a disconnected graph.

Note: A null graph that contains the 'n' number of vertices is also a form of a disconnected graph.

15. Cyclic Graph

Cyclic Graph is defined as the graph that contains n number of vertices where n is greater or equal to 3 (n> = 3).

Vertex: V1, V2, V3.....................Vn

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