Best Object Oriented approach to solve this simple scenario

I'm not so sure about what's the best approach to model this problem in the object oriented world.

Suppose I have to represent a graph and it's nodes in Java and suppose I to visit the graph using a depth first search (DFS).

What the best approach in Software engineering among these two:

• Create a class Node, a class Graph and a class GraphsFunctions where the GraphsFunctions class contains the DFS method which takes the Graph and a Node as parameters. Something like this: public void DFS(Graph g, Node n) and the call new GraphsFunctions().DFS(new Graph(), new Node())

• Create a class Node, a class Graph where the Graph class contains the DFS method which takes only the Node as parameter. Something like this: public void DFS(Node n) and the call new Graph().DFS(new Node())

I would rather use the first of the two options but I can't say why it's the best for me. Can you tell me what makes the best choice, actually the best?