Adjacency Matrices in Graph Theory

The video tutorial covers graph representation in data structures, focusing on adjacency matrices, symmetric properties, and examples of undirected, directed, and weighted graphs. It explains how to represent graphs using adjacency matrices, highlighting the differences between symmetric and non-symmetric matrices in undirected and directed graphs. The tutorial also provides examples of graph representations, including weighted graphs, and explains how to calculate adjacency matrices for different types of graphs.

What are the three types of graph representations mentioned?

• Adjacency Matrix, Incidence Matrix, Adjacency List

• Adjacency Matrix, Edge List, Vertex List

• Incidence Matrix, Edge List, Vertex List

• Adjacency List, Edge List, Vertex List

What is the size of the adjacency matrix for a graph with n vertices?

• n x n

• n x (n-1)

• (n-1) x (n-1)

• 2n x 2n

In an adjacency matrix, what does a value of 1 indicate?

• Presence of an edge between two vertices

• Absence of an edge between two vertices

• Presence of a loop

• Graph is directed

What does a zero in an adjacency matrix typically represent?

• Absence of an edge

• Presence of an edge

• Presence of a loop

• Graph is weighted

What is a key property of the adjacency matrix of an undirected graph?

• It is always one

• It is symmetric

• It is asymmetric

• It is always zero

What does a self-loop in an adjacency matrix indicate?

• A vertex is isolated

• A vertex has no connections

• A vertex is connected to itself

• A vertex is connected to all others

In an undirected graph, if there is an edge from A to B, what else is true?

• There is a loop at B

• There is a loop at A

• There is no edge from B to A

• There is an edge from B to A

What is the adjacency matrix of an undirected graph always?

• Zero

• One

• Asymmetric

• Symmetric

In an undirected graph, what does a 1 in the adjacency matrix from vertex A to B indicate?

• There is a loop at B

• There is a loop at A

• There is no edge between A and B

• There is an edge between A and B

In an undirected graph, if there is an edge from A to B, what else is true?

• There is an edge from B to A

• There is no edge from B to A

• There is a loop at B

• There is a loop at A