a.js

var ee = new (require('events').EventEmitter)()

function init () {
  console.log('initialize this function on require')
  setTimeout(function () {
    ee.emit('init', 'got called!')
  }, 2000)
}

init()
module.exports = ee

b.js

var a = require('./a.js')

function init () {
  a.on('init', function (string) {
    console.log('from b', string)
  })
}

module.exports = init

index.js

var a = require('./a.js')
var b = require('./b.js')

console.log('this is index.js')
b()

a.on('init', function (string) {
  console.log(string)
})