group-values.js

const headToTail = (i, v) => (v.substring(i) + v.substring(0, i));

const createSharedId = str => str
    .split('')
    .reduce((acc, a) => ([...acc, headToTail(acc.length, str.toLowerCase())]), [])
    .sort()[0];

const valueReducer = (acc, { src, sharedId }) => (typeof acc[sharedId] === 'undefined')
    ? { ...acc, [sharedId]: [src] }
    : { ...acc, [sharedId]: [ ...acc[sharedId], src] };

const toGroupedObj = arr => arr
    .map(v => ({ src: v, sharedId: createSharedId(v) }))
    .reduce(valueReducer, {});

const groupValues = arr => Object.values(toGroupedObj(arr));

// Use:
const result = groupValues(["Tokyo", "London", "Rome", "Donlon", "Kyoto", "Paris"]);
console.log(result); // [ [ 'Tokyo', 'Kyoto' ],[ 'London', 'Donlon' ],[ 'Rome' ],[ 'Paris' ] ]