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Table of contents
1.
Introduction
2.
Graphs
3.
Finite Graph
4.
Infinite Graph
5.
Trivial Graph
6.
Simple Graph
7.
Null Graph
8.
Complete Graph
9.
Pseudo Graph
10.
Regular Graph
11.
Bipartite Graph
12.
Labeled Graph
13.
Digraph Graph
14.
Subgraph
15.
Connected Graph
16.
Disconnected Graph
17.
Cyclic Graph
18.
Multi Graph
19.
Applications
20.
FAQs
21.
Key Takeaways
Last Updated: Mar 27, 2024
Easy

Graph Types and Applications

Author Saksham Gupta
0 upvote
Leveraging ChatGPT - GenAI as a Microsoft Data Expert
Speaker
Prerita Agarwal
Data Specialist @
23 Jul, 2024 @ 01:30 PM

Introduction

Graphs are the foundation of any coding interview. As a result, it is critical to have a solid understanding of this subject. But don't be concerned about any of it. Ninjas are here to help, and today we'll talk about different types of graphs and their applications.

 

Graphs

                                         source

A graph is represented by a series of dots that represent vertices (V) and are connected by lines or curves that represent edges (E).

Now let's discuss different types of graphs.

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Finite Graph

A graph is known as finite if it has a finite number of vertices and edges.

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Infinite Graph

A graph is known as infinite if it has an infinite number of vertices and edges.

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Trivial Graph

A graph is known astrivial if it has only one vertex and no edges.

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Simple Graph

A simple graph is one that comprises not more than one edge between two vertices. A set of railway tracks that connects two cities is an example of a simple graph.

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Null Graph

A null graph is a graph that consists only of isolated vertices.

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Complete Graph

A simple graph with 'N' vertices is known as complete graph if the degree of each vertex is N - 1, implying that one vertex is connected by N - 1 edges. Full Graph is another name for a complete graph.

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Pseudo Graph

A pseudo graph is a graph G with a self-loop and multiple edges.

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Regular Graph

A simple graph is known as regular if all of its vertices have the same degree. All complete graphs are regular, but the opposite is not true.

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Bipartite Graph

A bipartite graph (or bigraph) contains vertices that may be divided into two distinct and independent sets, {U} and {V}, with each edge connecting a vertex in {U} to one in {V}. A bipartite graph, on the other hand, is one that contains no odd-length cycles.

The two sets, {U} and {V}, can be compared to a two-color coloring of the graph: if all nodes in {U} are blue and all nodes in {V} are green, each edge will have endpoints of different colors, as required by the graph coloring problem.

        Set representation

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              Bipartite Graph

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Labeled Graph

A labeled graph is one in which the vertices and edges of a graph are labeled with a name, data, or weight. It is also known as a Weighted Graph.

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Digraph Graph

A digraph is a graph G = (V, E) with a mapping f that translates every edge onto an ordered pair of vertices (Vi, Vj). It is also referred to as a Directed Graph. An ordered pair is an edge between Vi and Vj with an arrow pointing from Vi to Vj (Vi, Vj).

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Subgraph

A subgraph of a graph G(V, E) is one in which V1(G) is a subset of V(G) and E1(G) is a subset of E(G), and each edge of G1 has the same end vertices as in G.

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Connected Graph

A graph is known as a connected graph if there is a path from any vertex 'U' to any vertex 'V' or vice versa.

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Disconnected Graph

If there is no path between any two vertices in a graph, it is said to be disconnected.

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Cyclic Graph

Graphs that form cycles are called cyclic graphs.

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Multi Graph

Any graph which contains some parallel edges but doesn’t contain any self-loop is called a multigraph.

                                        source

But, What are the applications of Graphs?

Applications

Graphs are used to describe communication networks, data organization, computing equipment, and so on. Graph theory is also utilized in chemistry and physics to investigate molecules. Graph theory is also used extensively in sociology. Graphs are useful in geometry and some sections of topology, such as knot theory. Graph theory has applications in biology and conservation as well.
Check out this problem - No of Spanning Trees in a Graph

FAQs

  1. What is a Graph?
    A graph is a non-linear data structure that consists of nodes and edges. The edges represent some form of connectivity between the nodes. Edges are lines or arcs that connect any two nodes in the network. Nodes are sometimes referred to as vertices.
     
  2. How do directed and undirected graphs differ?
    A directed graph has ordered pairings of vertices, whereas an undirected graph has unordered pairs of vertices. Edges in a directed graph represent the direction of vertices, but edges in an undirected graph do not.
     
  3. What is the maximum number of edges in the undirected graph of Nodes N? 
    In an undirected network, each node can have an edge over every other N-1 node. As a result, the total number of edges possible is N * (N - 1), yet in the undirected graph, the two edges between two nodes are the same. As a result, one of them must be removed. As a result, the total number of edges is N * (N - 1)/2.
     
  4. How can we Implement BFS?
    A queue can be used to implement BFS. We keep adding nodes from the same level to the queue and removing nodes from the previous level from the queue. When we finish traversing one level, all of the nodes for the next level are in the queue.
     
  5. Is there any other Data Structures and Algorithms content in Coding Ninjas Studio?
    Yes, you may practice coding as well as answer frequently requested interview questions in Coding Ninjas Studio. The more we practice, the more probable it is that we will land a position at our desired company.

Key Takeaways

In this article, we have extensively discussed the types of Graphs along with their applicationsWe hope that this blog has helped you enhance your knowledge of Graphs, and if you would like to learn more, check out our articles on Library. Do upvote our blog to help other ninjas grow. Happy Coding!

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