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Hajipur, Bihar, 844101
Python
Introduction to Python
Python Basics
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Python Syntax
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Python Comments
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Python Variables
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Python Data Types
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Python Casting
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Python I/O
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Python Operators
Cotrol Structures
Data Structures
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Python Strings
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Python Lists
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Python Tuples
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Python Dictionaries
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Python Sets
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Python Arrays
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Python Bytes and Bytearray
Date and Time
Functions and Module
File Handling
Python OOP
Advanced Concepts
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Python Scope
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Python Modules
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Python JSON
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Python RegEx
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Python PIP
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Python Try...Except
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Python String Formatting
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Python User Input
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Python VirtualEnv
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Python Math
Python DSA
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Python DSA
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Lists and Arrays
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Python Stacks
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Python Queues
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Linked Lists
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Python Hash Tables
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Python Trees
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Python Binary Trees
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Binary Search Trees
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Python AVL Trees
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Python Graphs
Searching Algorithms
Sorting Algorithms
Python Graphs
A Graph is a non-linear data structure that represents relationships between pairs of elements (called nodes or vertices) using edges.
Graphs can be:
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Directed or Undirected
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Weighted or Unweighted
🔹 Basic Graph Terms
| Term | Meaning |
|---|---|
| Vertex | A node in the graph |
| Edge | A connection between two vertices |
| Adjacent | Two vertices connected by an edge |
| Path | A sequence of vertices connected by edges |
| Degree | Number of edges connected to a node |
🔹 Representing a Graph in Python
1. Using Adjacency List (Dictionary)
graph = {
'A': ['B', 'C'],
'B': ['D'],
'C': ['E'],
'D': ['F'],
'E': [],
'F': []
}
2. Using Adjacency Matrix
vertices = ['A', 'B', 'C']
matrix = [
[0, 1, 1],
[0, 0, 0],
[0, 0, 0]
]
🔹 Depth-First Search (DFS)
def dfs(graph, node, visited):
if node not in visited:
print(node)
visited.add(node)
for neighbor in graph[node]:
dfs(graph, neighbor, visited)
visited = set()
dfs(graph, 'A', visited)
✅ Output:
A
B
D
F
C
E
🔹 Breadth-First Search (BFS)
from collections import deque
def bfs(graph, start):
visited = set()
queue = deque([start])
while queue:
vertex = queue.popleft()
if vertex not in visited:
print(vertex)
visited.add(vertex)
queue.extend(graph[vertex])
bfs(graph, 'A')
✅ Output:
A
B
C
D
E
F
🔹 Directed vs Undirected Graph
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Directed: Edges have direction → (
A → B) -
Undirected: Edges go both ways (
A — B)
🔹 Use Cases of Graphs
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Social networks (users connected to users)
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Maps and navigation (cities connected by roads)
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Web crawlers (pages connected via links)
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Network routing
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AI pathfinding (games, robotics)
Practice Questions
Q1. Write a Python program to create an undirected graph with 5 nodes using an adjacency list.
Q2. Write a Python program to implement a function to add new vertices to the graph.
Q3. Write a Python program to traverse the graph using Depth-First Search (DFS).
Q4. Write a Python program to traverse the graph using Breadth-First Search (BFS).
Q5. Write a Python program to count the number of connections (edges) for a given node.
Q6. Write a Python program to check if two nodes are connected directly.
Q7. Write a Python program to list all paths between two nodes using recursion or DFS.
Q8. Write a Python program to convert an adjacency list into an adjacency matrix.
Q9. Write a Python program to mark and print all visited nodes during a DFS traversal.
Q10. Write a Python program to create a weighted undirected graph using a dictionary of dictionaries or a tuple-based structure.
Python
Introduction to Python
Python Basics
-
Python Syntax
-
Python Comments
-
Python Variables
-
Python Data Types
-
Python Casting
-
Python I/O
-
Python Operators
Cotrol Structures
Data Structures
-
Python Strings
-
Python Lists
-
Python Tuples
-
Python Dictionaries
-
Python Sets
-
Python Arrays
-
Python Bytes and Bytearray
Date and Time
Functions and Module
File Handling
Python OOP
Advanced Concepts
-
Python Scope
-
Python Modules
-
Python JSON
-
Python RegEx
-
Python PIP
-
Python Try...Except
-
Python String Formatting
-
Python User Input
-
Python VirtualEnv
-
Python Math
Python DSA
-
Python DSA
-
Lists and Arrays
-
Python Stacks
-
Python Queues
-
Linked Lists
-
Python Hash Tables
-
Python Trees
-
Python Binary Trees
-
Binary Search Trees
-
Python AVL Trees
-
Python Graphs
Searching Algorithms
Sorting Algorithms
