Avoiding the same answer multiple times in prolog

Question

So I have this undirected graph to traverse, and I should find all the verticies those are connected to a given vertex.

edge(a, b).
edge(b, c).
edge(c, d).
edge(d, e).
edge(e, f).
edge(f, d).
edge(d, g).
edge(g, f).
edge(g, h).
edge(h, i).
edge(i, j).
edge(j, d).
edge(d, k).
edge(l, m).
edge(m, n).

undirectedEdge(X, Y) :- edge(X, Y).
undirectedEdge(X, Y) :- edge(Y, X).

connected(X, Y) :- undirectedEdge(X, Y).
connected(X, Y) :- connected(X, Z), connected(Z, Y), X \= Y.

And once I type connected(a, X). it goes into an infinite loop. I understand why I have it, but I have no idea how to avoid it, maybe I can find some help here?

Answer 1

Using closure0/3 and setof/3 we get:

connected(A,B) :-
   setof(t, closure0(undirectedEdge, A, B), _).

Answer 2

And once I type connected(a, X). it goes into an infinite loop.

The reason this happens is because it is checking a path of the form a → b → a → b → a → b → …. So it keeps "hopping" between two nodes.

You can maintain a list of nodes that the algorithm already visisted, to prevent that like:

connected(X, Y) :-
    connected(X, Y, [X]).

connected(X, X, _).
connected(X, Z, L) :-
    undirectedEdge(X, Y),
    \+ member(Y, L),
    connected(Y, Z, [Y|L]).

You can make use of the distinct/1 predicate [swi-doc] to generate distinct answers:

?- distinct(connected(a, X)).
X = a ;
X = b ;
X = c ;
X = d ;
X = e ;
X = f ;
X = g ;
X = h ;
X = i ;
X = j ;
X = k ;
false.