Inserting a node in a directed graph is a constant time operation, typically O(1), as it involves creating a new vertex.
Deleting a node in a directed graph requires updating adjacency lists and removing connected edges. The time complexity is O(d + e), where d is the out-degree of the node and e is the total number of edges.
Inserting an edge involves updating the outgoing edges of the source node, resulting in a time complexity of O(1).
Deleting an edge in a directed graph is a constant time operation, typically O(1), as it involves removing the directed connection between two nodes.
Depth-First Search (DFS) is a graph traversal algorithm that explores as far as possible along each branch before backtracking. It starts at an initial node, visits adjacent nodes, and continues deeper until it reaches a leaf node. Then, it backtracks and explores other branches. DFS has a time complexity of O(V + E), where V is the number of vertices and E is the number of edges in the graph.
Breadth-First Search (BFS) is a graph traversal algorithm that systematically explores all the vertices at the current level before moving on to the next level. Starting from an initial node, BFS visits its neighbors, then the neighbors' neighbors, and so on, until all reachable nodes are visited. The time complexity of BFS is O(V + E), where V is the number of vertices, and E is the number of edges in the graph.
