Java: Object that gives reference to ArrayList<Objects> from the same class

Prefer not using the list passed in, but rather copy its contents:

public void setNeighbours(ArrayList<Node> neighbours){
    this.neighbours.clear();
    this.neighbours.addAll(neighbours);
}

because if you use it, another process could change it without your class knowing about the change.

Yes you can create a default constructor.

public Node() {}

That way you can just create an empty node

Node A = new Node();

And still use the class as you described

Node A = new Node(listOfNeighbors);

Also for your set method for your newly created empty nodes, I'd recommend using something like Bohemian posted, ie copying the list contents passed in after clearing your member lists contents: https://stackoverflow.com/a/20847517/772385

If I'm interpreting your question correctly, you've already done it. If you want to refer to Node A as Node A, simply put A (the name of the variable) in your code. When you want its neighbours, simply put A.getNeighbours() in.

Node A is a Node. The neighbours are a mere property (field) of that node. This means that referring to the node by its name means it is being used as a node. Using it in tandem with getNeighbours() means it is being used as an array (in your example, [B, C])

I'm not sure this is completely what you're asking, but what you probably need is some kind of data field in each node. That way you can identify the Node based on it's data as opposed just a list of the nodes it connects to. As it stands now, you would only be able to search through then based on their connections because they don't have any identifying properties.

Not sure answer your question but the first step is to define the graph through the edges, like a linked list, indicating the source node and the destination node. Then to perform the algorithm dfs you got that mark the path neighbor, not again pass by him, so that each node should have an attribute name and a state.

public class DephFirstSearch {
            Vertex vertice[];
            ArrayList list=new ArrayList();
            public DephFirstSearch(int  tam,ArrayList list)
            {
                    vertice = new Vertex [tam];
                    vertice[0]= new Vertex("V0", false);
                    vertice[1]= new Vertex("V1", false);
                    vertice[2]= new Vertex("V2", false);
                    vertice[3]= new Vertex("V3", false);
                    vertice[4]= new Vertex("V4", false);
                    vertice[5]= new Vertex("V5", false);
                    vertice[6]= new Vertex("V6", false);

                    this.list=list;                 

            }
            public void dfs(String origen) {

                    dfsVisit(vertice[0], 0);
            }
            public void dfsVisit(Vertex nodo, int i) {
                    nodo.setState(true);
                    System.out.println("nodo: " + nodo.getNode());

                    for (int j = 0; j < vertice.length; j++) {
                            if (isEdge(i, j) && vertice[j].isState() != true) {
                                    dfsVisit(vertice[j], j);
                            }
                    }

            }

            public boolean isEdge(int i, int j) {
                    Vertex actual = vertice[i];
                    Vertex next = vertice[j];
                    Vector lac;

                    for (int k = 0; k < list.size(); k++) {
                            lac = (Vector) list.get(k);
                            if (lac.getOrigin().equals(actual.getNode())
                                            && lac.getDestination().equals(next.getNode())) {
                                    return true;

                            }

                    }

                    return false;

                }

    public class Vertex 
  {
            String node;
            boolean state;

            public Vertex(String node, boolean state) {
                    super();
                    this.node = node;
                    this.state = state;`enter code here`
            }
}

If you change the constructor parameter to Array like this:

public Node(Node... nodes){ }

you can pass something like this:

Node A = new Node(b,c);

inside the constructor you should write like this: Arrays.asList(nodes) and it returns List