Understanding Graph Representation Techniques

What is an adjacency matrix in graph theory?

• A list of all the edges in a graph.

• A collection of linked lists, each representing the neighbours of a vertex.

• A matrix that only represents weighted graphs.

Which of the following is a characteristic of an adjacency list?

• It uses more space than an adjacency matrix for sparse graphs.

• It is a 2D array representation of a graph.

• It is efficient in terms of space for representing sparse graphs.

• It cannot represent weighted graphs.

How is a weighted graph different from an unweighted graph?

• A weighted graph has edges with no values.

• A weighted graph has edges with associated values or weights.

• An unweighted graph can only be represented using an adjacency matrix.

• A weighted graph cannot be represented using an adjacency list.

In an adjacency matrix, what does a value of 0 typically represent?

• The presence of an edge between two vertices.

• The absence of an edge between two vertices.

• The weight of an edge between two vertices.

• The total number of edges in the graph.

Which graph representation is generally more space-efficient for dense graphs?

• Adjacency list

• Adjacency matrix

• Edge list

• Incidence matrix

What is the primary advantage of using an adjacency list over an adjacency matrix?

• Faster to check if an edge exists between two vertices.

• More space-efficient for dense graphs.

• More space-efficient for sparse graphs.

• Easier to implement in programming languages.

• The total number of edges in the graph.

Which of the following is true for an unweighted graph?

• All edges have the same weight.

• Edges do not have any associated weights.

• It can only be represented using an adjacency matrix.

• It cannot be represented using an adjacency list.

What is a key disadvantage of using an adjacency matrix?

• It is difficult to implement.

• It uses more space for sparse graphs.

• It cannot represent weighted graphs.

• It is slower to check if an edge exists between two vertices.

Which of the following is a correct statement about graph representation?

• An adjacency list is always more space-efficient than an adjacency matrix.

• An adjacency matrix is always more space-efficient than an adjacency list.

• An adjacency list is more space-efficient for sparse graphs, while an adjacency matrix is more space-efficient for dense graphs.

• Both adjacency lists and matrices are equally space-efficient for all types of graphs.