**Graph Theory** is the study of graphs that are concerned with the relationship between edges and vertices. It is a popular subject that has its applications in computer science, biosciences, information technology, mathematics and linguistics to mention but a few.

**A Graph** is a pictorial representation of a set of objects in which some pairs of objects are joined together by links. The linked objects are represented by points referred to as vertices, and the links that connect the vertices are termed edges.

**In Computer Science, Graphs are mostly used to represent various networks of communication,** the flow of computation, data organization, computational devices, etc. For example, the links of a website can be represented by a directed graph, where the vertices are used to represent web pages and the directed edges represent the links from one page to another.

**Graph Theory approach can be employed to solve problems in social media,** biology, travel, mapping the progression of neurodegenerative diseases, computer chip design, and a large number of other fields. The development of algorithms to manage graphs is therefore of significant interest in the study of computer science.

**The Transformation of Graphs** is frequently formalized and described by graph rewrite systems. Equivalent to graph transformation systems that are focusing on rule-based in-memory manipulation of graphs are graph databases that are geared towards transaction-safe, querying of graph-structured data and persistent storing.

**A Graph Structure** can be stretched and extended by assigning a weight to the edge of each of the graphs. Weighted graphs or graphs with weight, are applied to represent structures in which pairwise connections and links have some numerical values. Take, for example, if a Graph represents a road network, the weights could describe the length of each road. There may be several weights that are associated with each edge, which includes distance as seen in the previous example, Time of travel, or monetary cost. Such weighted graphs are mostly used to program GPS's, and search engines for travel-planning that compare flight times, hours and costs.

**There are many Features of Graph Theory and some of them are**

**1. Vertex:** A vertex or node v is simply a terminal point or a point of intersection on a graph. A vertex is the abstraction of Individual locations, for example, an administrative division, a city, an intersection on a road or a transport terminal, for example, stations, harbors, terminals, and airports.

**2. Edge (Link):** An edge is a connection between two nodes. A link is the reflection of a transport infrastructure that supports the movements between nodes. It has a direction that is generally represented on a graph as an arrow. Wherever an arrow is not used, it is considered that the link is bi-directional.

**3. Sub-Graph**: A sub-graph is a subset of a graph. Unless the general transport system is viewed in its whole, every transport network is, in theory, simply a sub-graph of another graph. For example, the road transportation network of a city is a sub-graph of a regional transportation network, which is on its own, a sub-graph of a national transportation network.

**4. Simple graph:** A simple graph is one that includes only one kind of link between its nodes. A road or terminal network is an example of a simple graph.

**There are lots of benefits of Graph Theory, some of them are:**

1. Graph Theory is very beneficial in Software engineering.

2. Graph Theory is used in Networking.

3. Graph Theory is fundamental in Data mining.

4. Graph Theory is employed in Operating system design.

5. Graph Theory is used Website designing to link websites and webpages.

1. It is elegant and it provides a framework to model a large set of problems in Computer Science.

2. It has natural connections to Combinatorics, Topology & Algebra.

3. It is essential for Data Science.

4. Job Opportunity and Career Advancement.

5. Entrepreneurship Opportunity and Consultancy.

Graph Theory - Home

Graph Theory - Introduction

Graph Theory - Fundamentals

Graph Theory - Basic Properties

Graph Theory - Types Of Graphs

Graph Theory - Trees

Graph Theory - Connectivity

Graph Theory - Coverings

Graph Theory - Matchings

Graph Theory - Independent Sets

Graph Theory - Coloring

Graph Theory - Isomorphism

Graph Theory - Traversability

Graph Theory - Video Lectures

Graph Theory - Exams and Certification

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