LeetCode 133 Clone Graph - Problem Statement

You're given a node in a connected undirected graph. Each node contains a value and a list of neighbors. Your task: return a deep copy of the graph.

This means creating completely new node objects with the same values and connections as the original. If node $1$ connects to node $2$ in the original, your copied node $1$ must connect to your copied node $2$.

The challenge: as you traverse the graph with DFS, how do you avoid creating duplicate copies of the same node? If node $1$ and node $2$ both reference node $3$, you need exactly one copy of node $3$.