**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
