Adjacency list representation, Data Structure & Algorithms

Assignment Help:

Adjacency list representation

An Adjacency list representation of Graph G = {V, E} contains an array of adjacency lists mentioned by adj of V list. For each of the vertex u?V, adj[u] contains all vertices adjacent to u in the graph G.

Consider the graph of Figure.

636_Adjacency list representation.png

Figure: A Graph

Given is the adjacency list representation of graph of above Figure:

adj [1] = {2, 3, 5}

adj [2] = {1, 4}

adj [3] = {1, 4, 5}

adj [4] = {2, 3, 5}

 adj [5] = {1, 3, 4}

An adjacency matrix representation of a Graph G=(V, E) is a matrix

The adjacency matrix for the graph of Figure is following:

 

1

2

3

4

5

1

0

1

1

0

1

 

2

 

1

 

0

 

0

 

1

 

1

 

3

 

1

 

0

 

0

 

1

 

1

 

4

 

0

 

1

 

1

 

0

 

1

 

5

 

1

 

0

 

1

 

1

 

0

 

 

 

 

 

 

Observe that the matrix is symmetric along the main diagonal. If we described the adjacency matrix as A and the transpose as AT , then for undirected graph G as above, A = AT.


Related Discussions:- Adjacency list representation

Searching, Searching is the procedure of looking for something: Finding one...

Searching is the procedure of looking for something: Finding one piece of data that has been stored inside a whole group of data. It is frequently the most time-consuming part of m

What are the languages which support assertions, What are the languages whi...

What are the languages which support assertions Languages which support assertions often provide different levels of support. For instance, Java has an assert statement which t

Data structure arrays, In this unit, we learned the data structure arrays f...

In this unit, we learned the data structure arrays from the application point of view and representation point of view. Two applications that are representation of a sparse matrix

An algorithm to insert a node in beginning of linked list, Q. Write down an...

Q. Write down an algorithm to insert a node in the beginning of the linked list.                         Ans: /* structure containing a link part and link part

Process of in-order traversal, In-order Traversal  This process when ex...

In-order Traversal  This process when executed iteratively also needs a stack and a Boolean to prevent the implementation from traversing any portion of a tree twice. The gener

Define complete binary tree, Define Complete Binary Tree Complete Binar...

Define Complete Binary Tree Complete Binary Tree:- A whole binary tree of depth d is that strictly binary tree all of whose leaves are at level D.

What are the different ways of representing a graph, What are the different...

What are the different ways of representing a graph? The different ways of representing a graph is: Adjacency list representation: This representation of graph having of an

Define doubly linked list, A list item stores pointers and an element ...

A list item stores pointers and an element to predecessor and successor. We call a pointer to a list item a handle . This looks simple enough, but pointers are so powerful tha

Design a binary search tree, Binary Search Tree usage: Write a progra...

Binary Search Tree usage: Write a program to compare the time taken for a search in a skewed tree, a balanced tree, and a random tree. Speci cally, your program should do the

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd