📘 Graph Algorithms in Python

Graph algorithms are fundamental in solving complex problems in computer science, such as pathfinding, network analysis, and optimization. Python, with its simplicity and rich libraries, is a popular choice for implementing these algorithms. Below are some common graph algorithms and their implementations in Python.

🧠 Key Concepts & Algorithms

1. Breadth-First Search (BFS)

   • A traversal algorithm that explores all neighbors at the present depth before moving to nodes at the next depth level.
   • 💡 Example:

     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)  
                 for neighbor in graph[node]:  
                     queue.append(neighbor)  
         return visited  
     

   

2. Depth-First Search (DFS)

   • Explores as far as possible along each branch before backtracking.
   • 🌐 Explore DFS implementation in Python for detailed code examples.

3. Dijkstra's Algorithm

   • Finds the shortest path in a weighted graph with non-negative edges.
   • ⏱️ Time complexity: O(V log V) (with priority queue).
   

4. Kruskal's Algorithm

   • Used for finding a Minimum Spanning Tree (MST) in a graph.
   • 🔧 Requires sorting edges and using a Union-Find data structure.

5. Prim's Algorithm

   • Another MST algorithm, but starts from a node and grows the tree dynamically.
   • 📈 Efficient for dense graphs.

📚 Resources for Further Learning

• Graph Theory Basics to understand the mathematical foundation.
• Visualizing Graph Algorithms with interactive diagrams.

📌 Example Use Cases

• Social network analysis (e.g., finding friends of friends).
• Routing protocols in computer networks.
• Scheduling tasks with dependencies.

Let me know if you'd like to dive deeper into any specific algorithm! 🚀