Graph Representation Techniques

The video tutorial discusses two popular methods for representing graphs in computers: adjacency matrix and adjacency list. It explains how each method works, their space complexities, and when to use them based on graph density. The adjacency matrix is suitable for dense graphs, while the adjacency list is better for sparse graphs. The tutorial also touches on the concept of loops in graphs and provides examples to illustrate the methods.

What are the two most popular methods for representing a graph in a computer?

• Graph tree and node map

• Edge list and vertex matrix

• Incidence matrix and path list

• Adjacency matrix and adjacency list

Which method uses a matrix to represent graph connections?

• Adjacency list

• Adjacency matrix

• Edge list

• Vertex map

In an adjacency matrix, what do the diagonal elements represent if there are no loops?

• They represent the number of vertices

• They are all 1

• They are all 0

• They represent the number of edges

What does an adjacency matrix entry of 1 indicate?

• A self-loop

• No connection between vertices

• A connection between vertices

• A loop at a vertex

What does a 0 in an adjacency matrix indicate?

• A loop at a vertex

• No connection between vertices

• A self-loop

• A connection between vertices

What does the adjacency matrix contain for each pair of vertices?

• The weight of the edge between them

• The vertices themselves

• The edges between them

• A 1 if they are connected, otherwise 0

What does a 1 in an adjacency matrix indicate for directed graphs?

• No connection between vertices

• A self-loop

• A connection from the column vertex to the row vertex

• A connection from the row vertex to the column vertex

How are edges represented in an adjacency matrix?

• As entries in a matrix

• As elements in linked lists

• As rows in a matrix

• As nodes in a tree

What does a 0 in an adjacency matrix indicate for directed graphs?

• A connection from the row vertex to the column vertex

• A connection from the column vertex to the row vertex

• No connection between vertices

• A self-loop

How is an adjacency list structured?

• As a tree structure

• As linked lists for each vertex

• As a list of edges

• As a matrix