Let’s see how it works pictorially;

Let’s pick a random node to start the traversal, let it be 2 (You can choose any node).

Now, visit any of its neighbour nodes (neighbors of 2 are 1,4) and pick any of its neighbourhood nodes.

Note: Now the Output console has 2 as the answer.

Now, let's say the algorithm picks 4.

Note : Now the Output console has 2,4 as the answer.

Now the algorithm checks for the unvisited neighbours of node 4, node 4 has only one unvisited neighbour node i.e 1 , So 1 will be visited.

Now, neighbours of 1(3,4) that are not visited will be visited, which means repetition of the same process which we did for previous nodes.

Note : Now the Output console has 2,4,1 as the answer.
Now let's assume the algorithm picks 3, so 3 will be visited.

Once 3 has been visited, there are no neighbour nodes for 3 which are to be visited so it will backtrack to 1.

Note : Now the Output console has 2,4,1,3 as the answer.

Now the algorithm is at node 1, when it checks for unvisited neighbours it will only find one node i.e 5, so it will visit 5 and backtrack to 1 as shown below.

Note: Now the Output console has 2,4,1,3,5 as the answer, Which is our expected answer!

When it backtracks to 1, now 1 has to backtrack to its previous node and this backtracking will happen till it reaches the start node.

Approach: <