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  1. Graphs are versatile data structures used to model relationships between entities. They consist of vertices (nodes) and edges (connections), and can be directed or undirected. Graph algorithms are essential for solving problems in areas like social networks, navigation systems, and network flows.

    Key Graph Algorithms

    1. Graph Traversal

    • Breadth-First Search (BFS): Explores all neighbors at the current depth before moving deeper. Ideal for finding the shortest path in unweighted graphs.

    • Depth-First Search (DFS): Explores as far as possible along each branch before backtracking. Useful for detecting cycles and connected components.

    from collections import deque

    # BFS Example
    def bfs(graph, start):
    visited = set()
    queue = deque([start])
    while queue:
    node = queue.popleft()
    if node not in visited:
    print(node, end=" ")
    visited.add(node)
    queue.extend(graph[node] - visited)

    # Example Graph
    graph = {
    'A': {'B', 'C'},
    'B': {'A', 'D', 'E'},
    'C': {'A', 'F'},
    'D': {'B'},
    'E': {'B', 'F'},
    'F': {'C', 'E'}
    }
    bfs(graph, 'A')
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