main.js

function Node (id, depth) {
  this.id = id;
  this.depth = depth;
  this.children = [];
  this.equals = function equals (otherNode) {
    return this.id === otherNode.id;
  };
}

function shortestPath (root, dest) {
  var current = root;
  var visited = [root];
  var valid = [];
  var counter = 0;

  while (!current.equals(dest)) {
    current.children.forEach(function (c) {
      if (visited.indexOf(c) > -1) {
        console.log('step #' + ++counter);
        console.log('skipping', c.id, 'since it has been visited');
        return;
      }
      console.log('step #' + ++counter);
      console.log(c.id);
      visited.push(c);
      valid.push(c);
    });
    current = valid.shift();
  }
}

var you = new Node("You", 0);
var a = new Node("a", 1);
var b = new Node("b", 1);
var c = new Node("c", 1);
var d = new Node("d", 2);
var e = new Node("e", 2);
var f = new Node("f", 3);

d.children.push(f);
c.children.push(d);
b.children.push(e);
b.children.push(c);
a.children.push(e);
a.children.push(b);
you.children.push(a);
you.children.push(b);
you.children.push(c);

shortestPath(you, f);

Copy and paste this to a directory on your machine, then run node main.js. You'll see the traversal play out step by step.