main.js

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

function shortestPath (root, dest) {
  var current = root;
  var visited = {};
  visited[root.id] = { hops: 0, prev: null };
  var valid = [];
  var counter = 0;
  var finalPath = [dest];
  var finalPrevious;

  while (!current.equals(dest)) {
    current.friends.forEach(function (c) {
      if (visited[c.id]) {
        console.log('step #' + (++counter));
        console.log('skipping', c.id, 'since it has been visited');
        return;
      }
      console.log('step #' + (++counter));
      console.log(c.id);
      visited[c.id] = {
        hops: visited[current.id].hops + 1,
        prev: current
      };
      valid.push(c);
    });
    current = valid.shift();
  }

  while (!finalPath[0].equals(root)) {
   finalPrevious = visited[finalPath[0].id].prev;
   finalPath.unshift(finalPrevious);
  }
  return finalPath;
}

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

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

console.log(shortestPath(you, f));

Obviously, one can examine the visited structure to see the number of hops along the way, or just get the length of finalPath after returning it.