visited = []
def BFS(start, target, GRAPH, depth, maxDepth):
  global visited
  #print "\t"*depth,start, "||", GRAPH[start], "||", [BFS(neighbor,target,GRAPH,depth+1,maxDepth) for neighbor in GRAPH[start]]
  if start not in visited:
    visited.append(start)
  else:
    print 'start: ',start,'visited: ', visited
    #you've already visited it, so ignore
    return maxDepth
  if target in GRAPH[start]:
    #you found it
    print 'start: ',start,'visited: ', visited,' and I found it'
    return depth+1
  else:
    if depth == maxDepth:
      print 'start: ',start,'visited: ', visited,' and I reached maxDepth'
      return maxDepth
    else:
      #you haven't found it, so run a BFS on the neighbors
      return min([BFS(neighbor,target,GRAPH,depth+1,maxDepth) for neighbor in GRAPH[start]])

print BFS(0,2,{0: [1,3], 1: [2], 2 : [0, 3], 3: [1]},0,3)