Last updated on September 4th, 2023 at 09:40 pm

Here, We will discuss about Graph Algorithms, types of nodes and graphs and also explain Graph Representation like Adjacency Matrix, Adjacency List and Graph Traversals like DFS and BFS.

**What is Graph?**

A** Graph** is a flow structure that represents the relationship between various objects. In other words, A graph is a pair **(V,E)** where V is number of **vertices** and E is number of **edges**.

Graph can be visualized by using the following two basic components:

**Nodes:**Nodes are entities whose relationships are expressed using edges.**Edges:**Edges are the components that are used to represent the relationship between various nodes in a graph.

**Types of Nodes in Graph**

**Root Node:**The root node is the ancestor of all other nodes in a graph. It does not have any ancestor. Root node has no parent.**Leaf Nodes:**Leaf nodes represent the nodes that do not have any successors.

**Types of Graphs**

**Undirected Graph:**An undirected graph is a graph in which all edges are bi-directional i.e, the edges do not point in any specific direction.**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.**Weighted Graph:**A weighted graph is a graph in which each edge is assigned a weight or cost.**Cyclic Graph:**A cyclic graph is a graph in which path that starts from a vertex and ends at the same vertex.

A

treeis an undirected graph in which any two vertices are connected by only one path.A tree cannot contains any cycles or self loops.

**Graph Representation**

Graph can represent in many ways. The two most common ways of representing a graph is as follow:

**Adjacency Matrix**

An adjacency matrix is 2D array of V*V vertices. Each row and column represent a vertex.

if the values of any elements ** a[i][j]** is 1, it represents that there is an edge connecting vertex i and vertex j.

**Adjacency List**

An adjacency list represents a graph as an array of linked lists.

It is efficient in terms of storage because we only need to store the values for the edges.

**Graph Traversals**

Graph traversal means visiting every vertex and edge exactly once in a well-defined order.

During a traversal, it is important that you track which vertices have been visited. The most common way of tracking vertices is to mark them

There are two such algorithm for traversing the graphs are:

### Related:

#### Depth First Search (DFS)

Here, We will discuss about Depth First Search (DFS), their algorithms and also explain advantages,…

#### Breadth First Search (BFS)

Here, We will discuss about Breadth First Search (BFS), their algorithms and also explain advantages,…

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