Graphs: A Comprehensive Guide to Network Structures for Data Structures and Algorithms

Question 1

What is a key advantage of using a graph compared to a tree data structure?

Accepted Answer

Graphs can represent complex relationships between objects.

Answer

Graphs are easier to implement than trees.

Answer

Graphs require less memory than trees.

Question 2

Which of these is NOT a fundamental operation on a graph?

Accepted Answer

Reversing the direction of the edges in a directed graph

Answer

Traversing the graph

Answer

Adding vertices

Answer

Calculating the shortest path between two vertices

Question 3

What is the time complexity of a breadth-first traversal of a graph with V vertices?

Accepted Answer

O(V)

Answer

O(E)

Answer

O(V^2)

Answer

O(E^2)

Question 4

What is the distinction between a weighted and an unweighted graph?

Accepted Answer

Weighted graphs have associated numerical values with their edges, while unweighted graphs do not.

Answer

Weighted graphs have no associated values with their edges, while unweighted graphs do.

Answer

Weighted graphs have edges that can be either directed or undirected, while unweighted graphs have only directed edges.

Answer

Weighted graphs can be represented using an adjacency matrix, while unweighted graphs cannot.

Question 5

What is the main difference between a directed and an undirected graph?

Accepted Answer

Directed graphs have a designated start and end vertex, while undirected graphs do not.

Answer

Directed graphs have weighted edges, while undirected graphs do not.

Answer

Directed graphs allow cycles, while undirected graphs do not.

Answer

Directed graphs can be represented using an adjacency matrix, while undirected graphs cannot.

Question 6

Which of the following algorithms is used to find the shortest path in a weighted graph?

Accepted Answer

Dijkstra's algorithm

Answer

Depth-first search

Answer

Breadth-first search

Answer

Prim's algorithm

Question 7

What property characterizes a strongly connected graph?

Accepted Answer

Every vertex can be reached from every other vertex

Answer

Some vertices cannot be reached from certain other vertices

Answer

The graph contains no cycles

Answer

The graph has no edges

Question 8

What is the purpose of a minimum spanning tree?

Accepted Answer

To find a subgraph that connects all vertices with the least total weight

Answer

To find the shortest path between two vertices in a graph

Answer

To find the longest path between two vertices in a graph

Answer

To find a subgraph with the most edges

Question 9

Which data structure is most suitable for representing a network of cities and the roads connecting them?

Accepted Answer

Graph

Answer

Array

Answer

Linked List

Answer

Hash Table

Question 10

What is the time complexity of performing a depth-first search (DFS) on a graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(E)

Answer

O(V^2)

Answer

O(E^2)

Question 11

Which of the following is a valid implementation of an adjacency list for a graph?

Accepted Answer

Array of linked lists

Answer

Array of arrays

Answer

Linked list of linked lists

Answer

Hash table of arrays

Question 12

What is the primary purpose of a minimum spanning tree (MST) in a graph?

Accepted Answer

To find a subset of edges that connects all vertices with minimum weight

Answer

To find the shortest path between two vertices

Answer

To find the longest path between two vertices

Answer

To find the most cycles in a graph

Question 13

Which graph traversal technique explores all vertices at the same level before moving to the next level?

Accepted Answer

Breadth-first search

Answer

Depth-first search

Answer

Topological sorting

Answer

Cycle detection

Question 14

What is the characteristic of a weighted graph?

Accepted Answer

Each edge has a numerical value associated with it

Answer

Each vertex has a numerical value associated with it

Answer

The number of edges is greater than the number of vertices

Answer

The number of vertices is greater than the number of edges

Question 15

Which algorithm is suitable for detecting cycles in a directed graph?

Accepted Answer

Depth-first search

Answer

Breadth-first search

Answer

Dijkstra's algorithm

Answer

Kruskal's algorithm

Question 16

What is the key difference between a tree and a connected graph?

Accepted Answer

A tree has no cycles, while a connected graph may have cycles

Answer

A connected graph has no cycles, while a tree may have cycles

Answer

A tree has a unique path between every pair of vertices, while a connected graph may have multiple paths

Answer

A connected graph has a unique path between every pair of vertices, while a tree may have multiple paths

Question 17

What is the degree of a vertex in a graph?

Accepted Answer

The number of edges it is connected to

Answer

The number of vertices it is connected to

Answer

The number of paths that start from it

Answer

The number of cycles that pass through it

Question 18

Which data structure effectively represents a collection of interconnected elements, including both nodes and the connections between them?

Accepted Answer

Graph

Answer

Tree

Answer

List

Answer

Array

Question 19

Regarding a graph with V vertices and E edges, what is the time complexity of performing a depth-first search?

Accepted Answer

O(V * E)

Answer

O(V)

Answer

O(E * V)

Answer

O(log(V))

Question 20

Which graph traversal algorithm is employed to determine the shortest path between two specified vertices?

Accepted Answer

Dijkstra's algorithm

Answer

Depth-first search

Answer

Breadth-first search

Answer

Bellman-Ford algorithm

Question 21

In graph representation, what is the primary purpose of an adjacency list?

Accepted Answer

Storing vertices along with their respective connections

Answer

Storing edges with their associated weights

Answer

Visually representing the graph structure

Answer

Calculating the shortest path between vertices

Question 22

Distinguish between directed and undirected graphs. Which key difference applies?

Accepted Answer

Directed graphs have a defined starting and ending vertex, a concept not present in undirected graphs

Answer

Directed graphs have weighted edges, while undirected graphs do not

Answer

Directed graphs allow multiple edges between the same pair of vertices, unlike undirected graphs

Answer

Undirected graphs possess a higher time complexity compared to directed graphs

Question 23

Which of the following graph algorithms is specifically designed to identify strongly connected components?

Accepted Answer

Tarjan's algorithm

Answer

Kruskal's algorithm

Answer

Prim's algorithm

Answer

Floyd-Warshall algorithm

Question 24

Which type of graph assigns numerical values to its edges?

Accepted Answer

A graph where each edge has a numerical value associated with it

Answer

A graph where the vertices are weighted

Answer

A graph where the edges are directed

Answer

A graph where the vertices are connected in a specific order

Question 25

Define the concept of a minimum spanning tree within a weighted graph.

Accepted Answer

A subgraph that encompasses all vertices and possesses the least total edge weight

Answer

A subgraph that encompasses all vertices and possesses the greatest total edge weight

Answer

A subgraph with the fewest possible edges

Answer

A subgraph with the longest possible path

Question 26

Which of the following is NOT a fundamental operation on graphs?

Accepted Answer

Intersection

Answer

Union

Answer

Breadth-first search

Answer

Topological sort

Question 27

In a depth-first search, what is the order in which nodes are visited?

Accepted Answer

Depth-first order

Answer

Breadth-first order

Answer

Topological order

Answer

Random order

Question 28

Which data structure is most commonly used to implement a graph?

Accepted Answer

HashMap

Answer

Array

Answer

LinkedList

Answer

Tree

Question 29

What is the time complexity of traversing a connected graph using BFS?

Accepted Answer

O(V + E)

Answer

O(V^2 + E)

Answer

O(V * E)

Answer

O(E^2)

Question 30

Which of the following applications of graphs is used to find the shortest path between nodes?

Accepted Answer

Dijkstra's algorithm

Answer

Minimum spanning tree

Answer

Euler's theorem

Answer

Topological sorting

Question 31

In a weighted graph, what is associated with the edges?

Accepted Answer

Weights

Answer

Nodes

Answer

Paths

Answer

Distances

Question 32

Which algorithm is specifically designed to detect cycles in directed graphs?

Accepted Answer

Tarjan's algorithm

Answer

Kruskal's algorithm

Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Question 33

What is the primary difference between directed and undirected graphs?

Accepted Answer

Directed graphs have one-way edges, undirected graphs have two-way edges

Answer

Directed graphs have two-way edges, undirected graphs have one-way edges

Answer

Directed graphs only have one-way edges, undirected graphs can have both one-way and two-way edges

Answer

Undirected graphs only have one-way edges, directed graphs can have both one-way and two-way edges

Question 34

Which of the following is NOT a valid graph traversal method?

Accepted Answer

Binary search

Answer

Depth-first search

Answer

Breadth-first search

Answer

Recursive traversal

Question 35

What is the primary purpose of topological sorting?

Accepted Answer

To arrange nodes in a linear order that satisfies dependencies

Answer

To identify all nodes in the graph

Answer

To find the shortest path between nodes

Answer

To detect cycles in a graph

Question 36

Which graph algorithm is commonly used in image processing and computer vision applications?

Accepted Answer

Connected Components Algorithm

Answer

Minimum Spanning Tree

Answer

Dijkstra's Algorithm

Answer

Topological Sort

Question 37

Which of the following graph representations stores adjacent nodes in a linked list for each node?

Accepted Answer

Adjacency List

Answer

Incidence Matrix

Answer

Adjacency Matrix

Question 38

What is the time complexity of a depth-first search (DFS) on an undirected graph with n nodes and m edges?

Accepted Answer

O(n + m)

Answer

O(n^2)

Answer

O(m^2)

Question 39

Which of the following is a valid application of breadth-first search (BFS)?

Accepted Answer

Finding the shortest path in an unweighted graph

Answer

Finding a Hamiltonian cycle

Answer

Detecting cycles in a graph

Question 40

In a graph, the degree of a node represents:

Accepted Answer

The number of edges connected to it

Answer

The number of nodes connected to it

Answer

The distance to the nearest node

Question 41

Which algorithm can be used to find all the strongly connected components in a directed graph?

Accepted Answer

Kosaraju's Algorithm

Answer

Bellman-Ford Algorithm

Answer

Dijkstra's Algorithm

Question 42

What is the main purpose of a weighted graph?

Accepted Answer

To represent relationships with associated costs or weights

Answer

To represent relationships between infinite sets of objects

Question 43

Which property characterizes a tree?

Accepted Answer

It has n-1 edges, where n is the number of nodes

Answer

It is a connected graph

Answer

It has a maximum of n edges

Question 44

Which of the following is a valid application of a graph data structure?

Accepted Answer

Modeling social networks

Answer

Storing large amounts of text data

Question 45

What is the fundamental difference between a directed graph and an undirected graph?

Accepted Answer

Directed graphs have arcs, while undirected graphs have edges

Answer

Directed graphs are always connected, while undirected graphs are not

Question 46

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

Accepted Answer

Binary Tree

Answer

Weighted Graph

Answer

Directed Acyclic Graph (DAG)

Answer

Undirected Graph

Question 47

In a depth-first search (DFS), which data structure is typically used to keep track of visited nodes?

Accepted Answer

Stack

Answer

Linked List

Answer

Array

Answer

Queue

Question 48

What is the time complexity of a **breadth-first search (BFS)** on an **undirected graph** with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(V^2)

Answer

O(E log V)

Answer

O(E^2)

Question 49

In a directed graph, what does the **out-degree** of a node represent?

Accepted Answer

The number of edges leaving the node

Answer

The number of edges entering the node

Answer

The weight of the heaviest edge connected to the node

Answer

The total number of edges connected to the node

Question 50

Which of the following is a **necessary** condition for a graph to be acyclic?

Accepted Answer

It must not contain any cycles

Answer

It must have an even number of vertices

Answer

It must be a directed graph

Answer

It must be connected

Question 51

Consider a graph where each vertex represents a city and each edge represents a road connecting the cities. If the graph is connected, what can we conclude?

Accepted Answer

It is possible to travel between any two cities using only the roads represented in the graph

Answer

The graph must be weighted

Answer

The graph must be acyclic

Question 52

Which of the following is an **advantage** of using a graph to represent data compared to a table?

Accepted Answer

It can capture relationships between objects more efficiently

Answer

It requires less memory

Answer

It is easier to update