I have a vector in which I added some integer numbers. Now when I remove these numbers from the vector and try to store it in an int variable I am getting "Incompatible types..found int ,expected java.lang.object". Any suggestions how can I store the values in a vector in a variable.

Vector neig = new Vector();
    int x = neig.get(1); //error here

When you create a Vector without a type, it's automatically a Vector<Object> - that is, when you get() something from the vector, all the compiler knows is that it's an Object.

When you add() your ints, they're auto-boxed into Integers, which are of course Objects. Fine so far. When you get() them, though, they can't be auto-unboxed because to the compiler, they're not Integers, they're Objects.
You can cast them, if you want:

int x = (Integer)neig.get(1);

but what you're doing here is ignoring the wonderful world of Generics. If you really want to store your ints in a Vector, declare your Vector to be a Vector of Integers:

Vector<Integer> neig = new Vector<Integer>()

and the rest of the code should work fine.

Bear in mind, though, that you're paying a performance penalty for the autoconversion each time you add and get an int, and it might be better in terms of performance to use an array of ints.