Graph Representation: Master the Fundamentals for Advanced Data Structures

Question 1

Which representation is most appropriate for a graph with a limited number of edges?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 2

In an adjacency matrix representation, what is the time complexity of determining whether two nodes are connected?

Accepted Answer

O(1)

Answer

O(V)

Answer

O(E)

Question 3

Which representation is advantageous for sparse graphs in terms of space efficiency?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 4

Which representation is most suitable for sparse graphs, where the number of edges is significantly less than the number of vertices?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 5

For calculating the degree of a vertex in a graph, which representation provides the most efficient approach?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 6

What is the space complexity of an adjacency matrix representing a graph with V vertices and E edges?

Accepted Answer

O(V^2)

Answer

O(V)

Answer

O(E)

Question 7

Which of the following data structures is used to represent the edges of a graph as a list of tuples?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 8

In an adjacency matrix, what does a non-zero value typically represent?

Accepted Answer

The presence of an edge

Answer

An edge's weight

Answer

The absence of an edge

Question 9

In an adjacency matrix, the entry at [i, j] typically represents the:

Accepted Answer

Weight of the edge from vertex i to j

Answer

Weight of the edge from vertex j to i

Answer

Absence of an edge between i and j

Question 10

An entry of 0 in the incidence matrix usually indicates:

Accepted Answer

No edge between the corresponding vertex and edge

Answer

An edge between the corresponding vertex and edge

Answer

The weight of the edge

Question 11

When storing a sparse graph, which representation offers the best efficiency?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 12

In an adjacency list, what does each element represent?

Accepted Answer

A list of vertices adjacent to the corresponding vertex

Answer

A vertex

Answer

A weight associated with an edge

Answer

The degree of the corresponding vertex

Question 13

Which representation method is most efficient for representing sparse graphs?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 14

Which graph representation is most suitable for performing depth-first search?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 15

Identify the disadvantage of using adjacency lists to represent graphs.

Accepted Answer

Inefficient memory usage for dense graphs

Answer

Slow insertion and deletion of edges

Answer

Doesn't support efficient topological sort

Answer

Difficult to implement

Question 16

What is the primary purpose of weighted graphs?

Accepted Answer

Representing graphs with edge weights

Answer

Representing directed graphs

Answer

Representing undirected graphs

Answer

Representing bipartite graphs

Question 17

What is the objective of topological sorting?

Accepted Answer

Ordering vertices in a directed graph such that no vertex depends on any subsequent vertex in the order

Answer

Finding the shortest path between two vertices in a graph

Answer

Identifying all cycles in a graph

Answer

Determining if a graph is bipartite

Question 18

Which of the following is not a recognized type of graph?

Accepted Answer

Hypergraph

Answer

Directed graph

Answer

Undirected graph

Answer

Weighted graph

Question 19

Which data structure represents a graph as a collection of vertices and a set of edges connecting the vertices?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Answer

Weighted graph

Question 20

Which of the following graphs cannot be efficiently represented using an adjacency list?

Accepted Answer

Complete graph

Answer

Cycle

Answer

Bipartite graph

Answer

Tree

Question 21

What is the space complexity of representing a graph with n vertices and m edges using an adjacency matrix?

Accepted Answer

O(n^2)

Answer

O(n + m)

Answer

O(m)

Answer

O(n)

Question 22

What is the primary advantage of using an adjacency matrix to represent a complete graph?

Accepted Answer

Direct retrieval of all edges connected to a specific vertex.

Answer

Reduced complexity for shortest path calculations.

Answer

Optimized memory usage.

Answer

Improved efficiency in storing sparse graphs.

Question 23

Which of the following is NOT a valid graph representation?

Accepted Answer

Incidence list

Answer

Adjacency matrix

Answer

Adjacency list

Answer

Incidence matrix

Question 24

In an adjacency list, each node is represented by:

Accepted Answer

A list of its adjacent nodes

Answer

A matrix of its connections to other nodes

Answer

A single value representing its degree

Answer

A list of its incident edges

Question 25

An adjacency matrix represents a graph as:

Accepted Answer

A 2D array where cells indicate connections

Answer

A sparse matrix where non-zero values indicate edges

Answer

A list of lists where each sublist represents a node

Answer

A hash table where keys are nodes and values are adjacent nodes

Question 26

Which representation is most efficient for storing sparse graphs?

Accepted Answer

Adjacency list

Answer

Incidence matrix

Answer

Adjacency matrix

Question 27

In an adjacency list, the time complexity of finding a node's adjacent nodes is:

Accepted Answer

O(d)

Answer

O(log n)

Answer

O(1)

Answer

O(n)

Question 28

The adjacency matrix of a complete graph has:

Accepted Answer

All cells filled with non-zero values

Answer

Only the off-diagonal cells filled with non-zero values

Answer

All cells filled with zero values

Answer

Only the diagonal cells filled with non-zero values

Question 29

The time complexity of finding all edges incident to a node in an adjacency matrix is:

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(d)

Answer

O(1)

Question 30

Which graph representation is most suitable for depth-first search (DFS)?

Accepted Answer

Adjacency list

Answer

Incidence matrix

Answer

Hash table

Answer

Adjacency matrix

Question 31

Which graph representation data structure efficiently supports finding all nodes adjacent to a given node?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Linked list

Answer

Incidence matrix

Question 32

What is the time complexity of finding the number of edges in a graph represented as an adjacency matrix?

Accepted Answer

O(V^2)

Answer

O(V+E)

Answer

O(V)

Answer

O(E)

Question 33

Which graph representation is most suitable for representing a sparse graph?

Accepted Answer

Adjacency list

Answer

Breadth-first search tree

Answer

Adjacency matrix

Answer

Incidence matrix

Question 34

Which graph representation is most commonly used for pathfinding algorithms?

Accepted Answer

Adjacency list

Answer

Incidence matrix

Answer

Spanning tree

Answer

Adjacency matrix

Question 35

Given a graph represented as an adjacency list, what is the time complexity of finding the degree of a vertex?

Accepted Answer

O(1)

Answer

O(E)

Answer

O(V)

Answer

O(V^2)

Question 36

Which graph representation is suitable for representing directed graphs with multiple edges between vertices?

Accepted Answer

Adjacency list with parallel edges

Answer

Incidence matrix with edge directions

Answer

Edge list with vertex weights

Answer

Adjacency matrix with edge weights

Question 37

Which graph representation is most efficient for storing and accessing the neighbors of a vertex?

Accepted Answer

Adjacency list

Answer

Edge list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 38

In an adjacency matrix representing a graph, what does a value of 1 at position (i, j) indicate?

Accepted Answer

An edge exists between vertices i and j

Answer

The weight of the edge between vertices i and j is 1

Answer

Vertex i is adjacent to vertex j

Answer

The distance between vertices i and j is 1

Question 39

What is the space complexity of an adjacency list representation for a graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(E)

Answer

O(V)

Answer

O(V^2)

Question 40

Which graph representation is best suited for sparse graphs with a relatively small number of edges?

Accepted Answer

Adjacency list

Answer

Incidence matrix

Answer

Edge list

Answer

Adjacency matrix

Question 41

An incidence matrix for a graph with V vertices and E edges has dimensions of:

Accepted Answer

V x E

Answer

V x V

Answer

E x V

Question 42

Which of the following operations is generally more efficient using an adjacency list compared to an adjacency matrix?

Accepted Answer

Finding all neighbors of a vertex

Answer

Checking if an edge exists between two vertices

Answer

Calculating the degree of a vertex

Answer

Determining if the graph is connected

Question 43

Consider a directed graph with V vertices. What is the maximum number of edges possible in this graph?

Accepted Answer

V*(V-1)

Answer

V

Answer

V^2

Answer

V*(V+1)

Question 44

Which graph representation would be most appropriate for a graph where edge weights are important and efficient lookup of edge weights is required?

Accepted Answer

Adjacency matrix

Answer

Adjacency list

Answer

Incidence matrix

Answer

Edge list

Question 45

In an undirected graph represented by an adjacency matrix, the matrix is always:

Accepted Answer

Symmetric

Answer

Asymmetric

Answer

Diagonal

Answer

Identity

Question 46

Consider a graph with n vertices and m edges. Which representation would be more efficient for storing the graph if n >> m?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Answer

Edge list