LeetCode 133 Clone Graph - Strategy

You need to walk through the original graph and build a copy as you go. For each node you visit, create a new node with the same value. Then recursively visit each neighbor and connect the copies.

The tricky part: graphs can have cycles and shared neighbors. If nodes $1$ and $3$ both connect to node $2$, you must reuse the same copied node $2$ for both. You cannot create $2$ separate copies. Your strategy needs a way to remember which nodes you have already copied.