**Tutorial: Introduction to Graph Theory**

**Category:** Computer Science

**Details:**

Graph theory is a foundational concept in computer science and mathematics, focusing on the study of graphs, which are structures consisting of nodes (vertices) and edges (connections between nodes). This tutorial provides a comprehensive introduction to graph theory, covering essential topics such as:

1. **Graph Representation:**

– Different ways to represent graphs, including adjacency matrix and adjacency list.

2. **Types of Graphs:**

– Classification based on directed and undirected graphs, weighted and unweighted graphs, and cyclic and acyclic graphs.

3. **Graph Traversal:**

– Algorithms such as Depth-First Search (DFS) and Breadth-First Search (BFS) for exploring and searching graphs.

4. **Shortest Path Algorithms:**

– Dijkstra’s algorithm for finding the shortest paths from a source node to all other nodes in a weighted graph.

5. **Minimum Spanning Tree:**

– Prim’s and Kruskal’s algorithms for finding the minimum spanning tree of a connected, weighted graph.

6. **Applications of Graph Theory:**

– Real-world applications in computer networks, social networks, recommendation systems, and more.

**Example:**

“`python

# Example of graph representation using adjacency list

graph = {

‘A’: [‘B’, ‘C’],

‘B’: [‘C’, ‘D’],

‘C’: [‘D’],

‘D’: [‘C’],

‘E’: [‘F’],

‘F’: [‘C’]

}

# Example of BFS traversal

from collections import deque

def bfs(graph, start):

visited = set()

queue = deque([start])

while queue:

node = queue.popleft()

if node not in visited:

visited.add(node)

print(node, end=’ ‘)

queue.extend(graph[node] – visited)

print(“BFS traversal starting from node ‘A’:”)

bfs(graph, ‘A’)

“`

**Conclusion:**

Graph theory is a versatile and powerful tool with applications across various domains in computer science and beyond. This tutorial aims to equip learners with a solid foundation in understanding and applying graph theory concepts and algorithms