Graphs - Networks, Connections, and Relationships

// Common Graph Algorithms:

// 1. Breadth-First Search (BFS) - Explore level by level
function BFS(graph, start):
    queue = [start]
    visited = new Set([start])
    while queue is not empty:
        node = queue.dequeue()
        for neighbor in graph[node]:
            if neighbor not in visited:
                visited.add(neighbor)
                queue.enqueue(neighbor)

// 2. Depth-First Search (DFS) - Explore as deep as possible
function DFS(graph, node, visited = new Set()):
    visited.add(node)
    for neighbor in graph[node]:
        if neighbor not in visited:
            DFS(graph, neighbor, visited)

// 3. Dijkstra's Algorithm - Find shortest path in weighted graph
function dijkstra(graph, start):
    distances = {node: Infinity for all nodes}
    distances[start] = 0
    pq = PriorityQueue()
    pq.add(start, 0)

    while pq is not empty:
        current = pq.extractMin()
        for neighbor, weight in graph[current]:
            distance = distances[current] + weight
            if distance < distances[neighbor]:
                distances[neighbor] = distance
                pq.add(neighbor, distance)

    return distances