## Representation of Graph

Generally graph can be represented in two ways namely
adjacency lists(Linked list representation) and adjacency matrix(matrix).

### Adjacency List:

This type of representation is suitable for the undirected
graphs without multiple edges, and directed graphs. This representation looks
as in the tables below.

If we try to apply the algorithms of graph using the
representation of graphs by lists of edges, or adjacency lists it can be
tedious and time taking if there are high number of edges.

For the sake of the computation, the graphs with many edges
can be represented in other ways. In this class we discuss two ways of
representing graphs in form of matrix.

### Adjacency Matrix:

Given a simple graph G =(V, E) with |V| = n. assume that the
vertices of the graph are listed in some arbitrary order like v1, v2, …, vn.
The adjacency matrix A of G, with respect to the order of the vertices is
n-by-n zero-one matrix (A = [aij]) with the condition,

Since there are n vertices and we may order vertices in any
order there are n! possible order of the vertices. The adjacency matrix depends
on the order of the vertices, hence there are n! possible adjacency matrices
for a graph with n vertices. In case of the directed graph we can extend the
same concept as in undirected graph as dictated by the relation

If the number of edges is few then the adjacency matrix
becomes sparse. Sometimes it will be beneficial to represented graph with
adjacency list in such a condition.

**Solution:Let the order of the vertices be a, b, c, d, e, f**

Let us take a directed graph

**Solution:**

**Let the order of the vertices be a, b, c, d, e, f, g**

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