JSFiddle - React, Tailwind, and code Playground

HTML

<script src="http://underscorejs.org/underscore.js"></script>

JavaScript

var anObject = {
    "id": "1111",
    "name": "Outdoor Skiing",
    "parent_id": "1110",
    "parents": [
        {
           "id": "1000000",
           "name": "Media"
        },
        {
           "id": "1000001",
           "name": "Movies"
        },
        {
           "id": "1000002",
           "name": "Outdoor Movies"
        },
        {
            "id": "1000003",
            "name": "Adventurous Movies"
        }
    ]
};

var flip = function(theObject, newObject, offset) {
    offset ? offset++ : offset = 1;
    var newObj = theObject.parents[theObject.parents.length - offset];
    newObject ? newObj.children = newObject : newObj.children = theObject;
    if (offset < theObject.parents.length)
    {
        flip(theObject, newObj, offset);
        return;
    }
    console.log(newObj);
};

flip(anObject);