// starting at s
function solve(graph, s) {
  var solutions = {};
  solutions[s] = [];
  solutions[s].dist = 0;
  
  while(true) {
    var p = null;
    var neighbor = null;
    var dist = Infinity;
    
    
    for(var n in solutions) {
      if(!solutions[n])
        continue
      var ndist = solutions[n].dist;
      var adj = graph[n];
  
      for(var a in adj) {

        if(solutions[a])
          continue;
       
        var d = adj[a] + ndist;
        if(d < dist) {
   
          p = solutions[n];
          neighbor = a;
          dist = d;
        }
      }
    }
    
    //no more solutions
    if(dist === Infinity) {
        break;
    }
    
    //extend parent's solution path
    solutions[neighbor] = p.concat(neighbor);
    //extend parent's cost
    solutions[neighbor].dist = dist;
  }
  
  return solutions;
}
//create graph
var graph = {};

var layout = {
  'R': ['2'],
  '2': ['3','4'],
  '3': ['4','6','13'],
  '4': ['5','8'],
  '5': ['7','11'],
  '6': ['13','15'],
  '7': ['10'],
  '8': ['11','13'],
  '9': ['14'],
  '10': [],
  '11': ['12'],
  '12': [],
  '13': ['14'],
  '14': [],
  '15': []
}

//convert uni-directional to bi-directional graph
// var graph = {
//     a: {e:1, b:1, g:3},
//     b: {a:1, c:1},
//     c: {b:1, d:1},
//     d: {c:1, e:1},
//     e: {d:1, a:1},
//     f: {g:1, h:1},
//     g: {a:3, f:1},
//     h: {f:1}
// };

for(var id in layout) {
  if(!graph[id])
    graph[id] = {};
  layout[id].forEach(function(aid) {
    graph[id][aid] = 1;
    if(!graph[aid])
      graph[aid] = {};
    graph[aid][id] = 1;
  });
}

//choose start node
var start = '10';
//get all solutions
var solutions = solve(graph, start);

console.log("From '"+start+"' to");
//display solutions
for(var s in solutions) {
  if(!solutions[s]) continue;
  console.log(" -> " + s + ": [" + solutions[s].join(", ") + "]   (dist:" + solutions[s].dist + ")");
}

// From '10' to
//  -> 2: [7, 5, 4, 2]   (dist:4)
//  -> 3: [7, 5, 4, 3]   (dist:4)
//  -> 4: [7, 5, 4]   (dist:3)
//  -> 5: [7, 5]   (dist:2)
//  -> 6: [7, 5, 4, 3, 6]   (dist:5)
//  -> 7: [7]   (dist:1)
//  -> 8: [7, 5, 4, 8]   (dist:4)
//  -> 9: [7, 5, 4, 3, 13, 14, 9]   (dist:7)
//  -> 10: []   (dist:0)
//  -> 11: [7, 5, 11]   (dist:3)
//  -> 12: [7, 5, 11, 12]   (dist:4)
//  -> 13: [7, 5, 4, 3, 13]   (dist:5)
//  -> 14: [7, 5, 4, 3, 13, 14]   (dist:6)
//  -> 15: [7, 5, 4, 3, 6, 15]   (dist:6)
//  -> R: [7, 5, 4, 2, R]   (dist:5)