• Graphs are used to solve real-life problems that involve representation of the problem space as a network. Examples of networks include telephone networks, circuit networks, social networks (like LinkedIn, Facebook etc.).

• A graph is a common data structure that consists of a finite set of nodes (or vertices) and a set of edges connecting them.

• A pair (x,y) is referred to as an edge, which communicates that the x vertex connects to the y vertex.

Types of graphs:

Directed Graph :

• A directed graph is a graph in which all the edges are uni-directional i.e. the edges point in a single direction.

Undirected Graph :

• An undirected graph is a graph in which all the edges are bi-directional i.e. the edges do not point in any specific direction.

There are alot of representations of graphs are available, But most popular representations are :

Some Real World Applications :

• Graph theory is used to find shortest path in road or a network.

• In Google Maps, various locations are represented as vertices or nodes and the roads are represented as edges and graph theory is used to find the shortest path between two nodes.

• Graphs are used to define the flow of computation.

• Graphs are used to represent networks of communication.

• Graph transformation systems work on rule-based in-memory manipulation of graphs. Graph databases ensure transaction-safe, persistent storing and querying of graph structured data.

• Graphs are used to represent data organization.

Graphs may Look Like This :