transitivity.js

'use strict'

var tags = {
  'a': ['b', 'c', 'd'],
  'b': ['c', 'd'],
  'c': ['d'],
  'd': [],
  'e': [],
  'f': ['a']
}

let checked = {}

for (let v in tags) {
  if (
    typeof checked[v] === 'undefined' && // not checked yet
    tags[v].length > 0 // does even have children
  ) {
    if (!transitive(v, tags[v])) {
      console.log('NOT TRANSITIVE')
    }
  }
}

function transitive(v, rootSubTags) {
  checked[v] = true

  for (let i = 0; i < tags[v].length; i++) {
    let w = tags[v][i]
    console.log('w:', w, rootSubTags)
    if (rootSubTags.indexOf(w) === -1) {
      return false
    }

    if (tags[w].length === 0) {
      return true
    }

    console.log('Enter recursion')
    return transitive(w, rootSubTags)
  }
}

console.log('indices:', checked)