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What exactly is a graph?

Graph is a non-linear data structure consisting of vertices and edges. It is composed of a set of vertices (V) and a set of edges (E). The graph is denoted by G(V, E).

Components of a graph:

1.Vertices : Vertices are the fundamental units of the graph. Sometimes, vertices are also known as vertex or nodes.

2.Edges : Edges are drawn or used to connect two nodes of the graph. It can be ordered pair of nodes in a directed graph.

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Types of Graphs

Now that you’ve learned about what are graphs in data structures, you will learn about their various types. Here is the list of different types of graphs in data structure:

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Representation

Here are the two most common ways to represent a graph :
1. Adjacency Matrix
2. Adjacency List

Adjacency Matrix

An adjacency matrix is a way of representing a graph as a matrix of boolean (0’s and 1’s).

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Adjacency List

It is an array of lists that is used to store edges between two vertices.

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Traversal

To traverse a Graph means to start in one vertex, and go along the edges to visit other vertices until all vertices, have been visited.
The two most common ways a Graph can be traversed are:
1. Depth First Search (DFS)
2. Breadth First Search (BFS)

Depth First Search

Depth First Search is said to go "deep" because it visits a vertex, then an adjacent vertex, and then that vertex' adjacent vertex, and so on, and in this way the distance from the starting vertex increases for each recursive iteration.

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Breadth First Search

Breadth First Search visits all adjacent vertices of a vertex before visiting neighboring vertices to the adjacent vertices. This means that vertices with the same distance from the starting vertex are visited before vertices further away from the starting vertex are visited.

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Uses of graphs

1. Graphs are commonly used to represent social networks, such as networks of friends on social media.

2. Graphs can be used to represent the topology of computer networks, such as the connections between routers and switches.

Uses of graphs

3. Graphs are used to represent the connections between different places in a transportation network, such as roads and airports.

4. Graphs are used in Neural Networks where vertices represent neurons and edges represent the synapses between them.