Graphs can be represented in various ways based on the underlying data structure used to store the vertices and edges.

• **We introduce four data structures for representing a graph:**

- Edge List
- Adjacency List
- Adjacency Map
- Adjacency Matrix

## Edge List:

An **edge list** is a simple and straightforward way to represent a graph in which all vertex objects are stored in an unordered list * V*, and all edge objects are stored in an unordered list

*.*

**E**## Adjacency List:

An adjacency list is a popular data structure for representing graphs, where the graph is stored as an array of lists.

• Each element in the array represents a vertex in the graph, and the corresponding list contains the vertices that are adjacent to the given vertex.

• This data structure efficiently captures the connections and relationships between vertices in the graph.

**For example**:-

## ‣ Adjacency Matrix:

Let **G=(V,E)** be a graph with n vertices: **v _{1}**,

**v**,

_{2}**v**, ……

_{3}**V**. The adjacency matrix of G with respect to given ordered list of vertices is a

_{n}**nxn**matrix denoted by

**A(G)=(a**

_{ij})_{nxn}.such that,

## Undirected graph representation

## Directed graph represenation

In the above examples, 1 represents an edge from row vertex to column vertex, and 0 represents no edge from row vertex to column vertex.

**Q). Find the adjacency matrix M _{A} of undirected graph G shown in Fig:**

**Solution:**Since graph G consist of four vertices. Therefore, the adjacency matrix wills a 4 x 4 matrix. The adjacency matrix is as follows in fig: