The Depth-First Search (DFS) approach is one of the most intuitive ways to solve the graph cloning problem. Here, we will recursively explore each node starting from the root (Node 1) and keep a map to store already cloned nodes, ensuring each node is cloned once.

For each node, we:

• Check if the node is already cloned; if so, return the cloned instance to avoid cycles.
• Create a new copy of the node.
• Iteratively clone all its neighbors and add the clone references to the new node's neighbor list.
• Return the cloned node.

An alternative approach is to use Breadth-First Search (BFS), which is iterative in nature. Here, we utilize a queue to help explore each node level by level, preventing deep recursion and managing each node's clone in a breadth-wise manner.

In this BFS approach:

• We initialize a queue with the starting node.
• Use a map to store cloned nodes and a visited state.
• Iteratively process nodes from the queue—cloning nodes, establishing clone-linking relationships, and enqueuing unvisited nodes.
• Once the queue is empty, cloning and linking are complete.