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

For loop, for (i = 0; i sequence of statements } Here, the loop e...

for (i = 0; i sequence of statements } Here, the loop executes n times. Thus, the sequence of statements also executes n times. Since we suppose the time complexity of th

Describe commonly used asymptotic notations, Q.1 Compare two functions n 2 ...

Q.1 Compare two functions n 2 and 2 n for various values of n. Determine when second becomes larger than first. Q.2 Why do we use asymptotic notation in the study of algorit

Define merge sort, Define Merge Sort  Merge sort is a perfect example ...

Define Merge Sort  Merge sort is a perfect example of a successful application of the divide and conquer method. It sorts a given array A[0...n-l] by separating it into two ha

Illustrate hls colour model, HLS Colour Model  This model has the doub...

HLS Colour Model  This model has the double-cone representation shown in Figure 3.40. The three colour parameters in this model are called hue (H), lightness (L), and Saturati

Depth First Search Through Un-weighted Connected Graph , Q. Write down the ...

Q. Write down the algorithm which does depth first search through an un-weighted connected graph. In an un-weighted graph, would breadth first search or depth first search or neith

Inequalities, #question.show that the following inequality is correct or in...

#question.show that the following inequality is correct or incorrect. n!=O(n^n)

Infix notation to postfix notation, Which data structure is required to cha...

Which data structure is required to change infix notation to postfix notation?    Stack function is used to change infix notation to postfix notatio n

Binary search tree in ascending order, In order to get the contents of a Bi...

In order to get the contents of a Binary search tree in ascending order, one has to traverse it in In-order

Post order traversal, Post order traversal: The children of node are vi...

Post order traversal: The children of node are visited before the node itself; the root is visited last. Each node is visited after its descendents are visited. Algorithm fo

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